This is a good question.
The first port of call is to try and create the best trip possible. That's the most important part because, if you took acid or shrooms under less favorable conditions, it wouldn't matter which you took because the end result will be pretty similar. You want to provide the best conditions possible for your trip and so learning about psychedelics beforehand is really important.
Having said that, there is learning about psychedelics and then learning about psychedelics. One process happens prior to taking them and the other happens afterwards and no amount of research can prepare you for a psychedelic experience once you are thrown into one. I learned that after my first time. All the work you do before only gets you half way and while it means a lot, the rest is out of your hands for the most part thereafter. I try and look at it as me carrying myself up until the point of having a psychedelic experience. I bring myself to a location, I research the location, I make sure I have real psychedelics and do due diligence to make this so, I spend the week prior in a sort of therapeutic headspace to bring myself to a level ready to trip, I plan what I might do and what will be around me (especially if outdoors), food, water, shelter etc. Even things like the amount of time in the day (especially if outdoors) so that I don't end up in the pitch black trying to find my way back. After I carry myself to the final point I am released from that position and now I'm open to the experience. I know I've done enough to get myself to where I needed to be and with everything I need. I always tend to look back on this through a trip and especially afterwards and appreciate the time, care and effort I put in looking after myself in such a way.
Now for first time psychedelic use. I'm not sure if it really matters which one you take for a first time. Mushrooms provide a more natural high. Every time I take them it feels natural and more grounded in the relationship between me and the mushrooms. With LSD though I tend to notice the artificiality of the experience in that LSD is of course a synthetic substance. I think lots of other people notice this as well. However when you're in a full blown trip this isn't the most important thing that comes to mind! It's more something you reflect on afterwards and also before the peak. With LSD it always feels less natural although the more cleaner the acid the more natural it feels. I tend to have a more deeper connection to my organic existence on mushrooms. It's like you are putting a piece of yourself inside yourself and just amplifying it. It's not a foreign process. Whereas LSD for me anyway is like putting something outside of yourself inside of yourself. The head space is more lighter on mushrooms too, even at higher doses. I did 5 grams last year in silent darkness in a shepherds hut in the sticks and didn't feel heavy at all. I witnessed language disintegrate but at the same time I hadn't got to the point beyond language or complete ego dissolution and so I still had thoughts only they disintegrated half way through consolidating them and at that point they broke down like a gear grinding against another gear and into nothingness they went all while this grinding gear effect sounded like a shamanic chant or something similar. LSD helped me to piece together my traumatic childhood and made me realize I wasn't to blame. I could see all the pieces come together so the script of my life story made sense and everything fit together perfectly as it was meant to be without the side narrative projected onto me by the experiences I had been through and what I had been made to believe and assume was true. LSD changed my life. Nothing has ever come close, and probably ever will. I solved the story of my childhood. Actually I had been on this path all my life prior and already had a high level of understanding. LSD propelled me to new heights and broke away conditioning that had corrupted my high level of understanding.
LSD will challenge what you think reality is. And this isn't always a pretty affair. The best trips are often the ones with the most difficult experiences. When you are battling with shit you've harboured your entire life. Or never knew you had harboured for that matter. Can mushrooms do that? I think so although I've never had life changing experiences on them. They are more insightful in other ways in that they are more spiritual (for me anyway). The 5g in silent darkness I told you about also made me realize that we are all gifted with being smothered in love and acceptance and that the universe seeks for things to be this way. Almost like the notion of there being a God or creator but without the labels and with it being the universe as a whole as an awe inspiring entity that has intelligence. We are all held up and brought together by the innate connection we all share and that is something deeply woven into our condition. I also realized that everything is okay and that I can let go and I won't fall off the edge of the world. Everything is how it is meant to be. All this was spiritual though and not like how LSD provides you insight. LSD is more "BAM! TAKE THAT! YOU NEED THIS TO WAKE UP!" whereas mushrooms sends you messages as if it comes from the Earth in much more earthy way. You are receiving messages from a very important organism that comes from the ground yet has such intelligence and this relationship you have with it is significant.
I would start small and work your way up. Try a light dose first, around 100ug or maybe 1g of mushrooms. This will give you consciousness altering effects but nothing that will send you into the psychedelic realm nor will you feel like you've lost control (which is a key process in the psychedelic experience). In this altered state you will experience yourself differently, see things differently and your head space will be different, but not completely transformed. This is intentional. You ideally want to build up to a psychedelic experience so you can get a feel for the terrain and also best plan the more intense and heavier experiences later on. Slowly start tweaking the dose increasing it experience after experience until you reach the psychedelic sweet spot. All the while get a feel for what works best for you; set and setting, music, goals, company you keep, visual and tactile elements, ambience and lighting etc. You will no doubt gravitate to a particular state you want to find yourself in after taking psychedelics a few times. For me it's always in nature and with the goal of introspection and therapeutic benefits. Everybody is different.
I cannot recommend enough tripping outdoors, especially if you can find yourself in the mountains watching on towards a beautiful vista. This is indescribable on psychedelics. You really are blown away by the beauty of nature. I've sat and stared at awe inspiring views for hours on psychedelics unable to fathom what is before me. The second time I took LSD with a friend we found a spot overlooking snow capped mountains complimented with contrasting green fields (where the snow had melted because it was more in-land and so warmer) and a lake in front of that. We did nothing for several hours other than tell each other how amazing the view was. We wanted to do nothing except sit there and watch it as if we turned away it would all disappear. I also tried to cook some food with a portable stove and lost my shit because the fucking thing wouldn't keep lit and so I ended up throwing it around cursing the stove, which put my friend into hysterics. We did finally cook some oats though, which by then had tufts of grass in because I had launched the thing around for a few minutes in desperation.
Research, research, research. Be an intelligent first timer. You will get way more out of the experience.
I see all too often unprepared rushed and uneducated attempts at taking psychedelics and it blows me away how careless people can be. Taking them in unfamiliar places around unfamiliar people and doing stuff that just taxes them instead of opens them up to the potential they can afford. Also, just as important, make sure you're taking REAL psychedelics!
This is where yet more research comes in and knowing how to source, who to source from, what to look for and utilizing your street smarts and diligence to keep yourself and your friends safe and sound. Don't just score some shit because someone sprang up with something you want. Know what it is and who it is whose providing it. Know who recommended this person and even who recommended the person who recommended you to use this person. At the least, get a reagent testing kit and if you can, send a tab off for remote lab testing. Always err on the side of caution and always seek to refuse something for the chance to find something better and to amass a variety of sources and products you can then scrutinize. After all, it's going in your body and psychedelics when tainted are no laughing matter. I once got some acid that had apparently been on special offer and was being bulk sent out as an incentive to new buyers to buy the 'full version' product. It was NBOME. I ended up having to lie down all night because of severe breathing problems. I couldn't move fast or do anything that involved much effort otherwise I felt like I was suffocating. Couldn't get up or move my arms or legs unless really slowly. The psychedelic experience was more visual hallucinations and it was extremely heavy on the body, not just through suffocating me either. That was a scary experience although I knew to just remain calm and lay down to ease blood flow around my vitals.
It will probably never happen to you but it's not impossible and it's always something you have to consider. I wish psychedelics was a utopia with only benevolent forces supplying them to the world but in reality, it's a business and there's lots of people who through sheer greed choose to not vet the products they get or purely because they are criminals who truly deserve to be locked up for harming those who want to do no harm to others and want to simply trip.
Research, start low, get yourself in the best headspace you can beforehand and live a healthy lifestyle (to benefit the experience before and after), lots of preperation, lots of goal setting and the rest is history!