I don't really like recommending one or only a few drugs with little reasoning behind it, better to do a comparative analysis
A note of advice before reading my opinion and using it as a guide: intensity is dosage-dependent next to depending on other factors summed up as set and setting. The best we can talk about is tendencies of drug effects, averages. There are always chances that you react unusually favorable or UNfavorable to these drugs so keep that in mind. If you don't carefully build up your dose, then typically all bets are off.
Phenethylamines.
Mescaline: brilliant compound and always worth a try IMO, although I might consider it a little atypical as a psychedelic.
2C-D : very mild and easy unless you take a lot, the dose-response curve is not very representative of what other psychedelics have in store and I would be concerned that people would understimate other psychedelics after 2C-D.
2C-C / 2C-B / 2C-I: good to begin with cause they are gentle but for me they can certainly be beautiful and psychedelic, even entheogenic and dissociative at higher doses!
2C-E: seems to be better for advanced trippers. Can be very deep, serious, complex, rational... potentially a little too heavy. Although when used correctly, perhaps with supervision, it could be considered on par with LSD.
2C-P: way too long lasting, steep dose-response curve... powerful. In many ways meant for experienced trippers afaik.
2C-T-2 / 2C-T-7: absolutely gorgeous, but probably quite complex, rich and unpredictable in several ways for a beginner. Also some potential GI upset. Possible but it's more of a risk.
Other 2C-X: probably too obscure / unusual, not all-round winners with potential to be unrepresentative for a psychedelic. Even if it is a winner like say 2C-EF seems to be, it is probably ideal to start out with a compound that is not too experimental, and has a fair body of human experience to rely on, compare with, research, etc.
NBOMe type drugs: I don't consider them safe or okay even with plenty of experience let alone for a beginner. What an experienced tripper wants to carefully experiment with is his/her business (keeping dosing limits in mind!), but a beginner ought to start with something else. Availability or price shouldn't play too big of a role in choosing a first psychedelic to trip on by the way.
Tryptamines.
Mushrooms: My first times ever were with mushrooms and the second time was an experience similar to what Peppersocks reported a little higher on this very page. I agree completely about the 'deep' part, it is IMO very much like being thrown in the deep end. I would personally NOT recommend mushrooms for a beginner at all. A number of full-on tryptamines are better to ease into after picking up a bit of experience keeping your mind steady.
4-AcO-DMT: I think similar things apply as with mushrooms, for me it seems smoother but at the same time I tend to go at least as deep without even realizing it. Has quality, but must not be underestimated and handled with extra care!
4-AcO / 4-HO-MET: probably preferred over mushrooms and I guess not that bad for a beginner! A lot of people seem to report that it is a lot less soul-rapey, mind-fucking and sinister / emotional rollercoaster. Instead it offers a lot mushrooms have to offer for me, but a lot more positives than negatives, combined with more stability.
4-AcO / 4-HO-MiPT: for a beginner somewhere in between mushrooms and 4-HO-MET in my opinion. It is a pretty strange ride for me, but the difficulty is no more than moderate I'd say.
4-AcO / 4-HO-DiPT: In my experience a more fun, easy and light trip than most other tryptamines mentioned thus far. There seems to be at least as much potential for body weirdness for a number of people, so it needs attention there.
DMT / DPT and similar ones: It is hard for any person to be prepared for psychedelics like these, but I consider them very heavy caliber trips... vaporized DMT doesn't last that long and is mostly a 'flash' so people can get away with it before getting stuck in a messed up place (although incidents happen!), some people report being to stupefied to even react with emotions like fear, if the duration is extended my opinion on mushrooms may apply.
DPT is in my opinion NOT for beginners, it often seems to be very rough and it lasts quite a bit longer than DMT.
5-MeO tryptamines: they tend to have different actions besides the classic action of psychedelics (5-HT2A agonism), like reuptake inhibition of a few monoamines and 5-HT1A agonism. I won't go far into the tendencies these drugs seem to produce like stimulation and slightly atypical entheogenic qualities... but I personally don't consider them very appropriate for a beginner or representative for most other psychedelics for that matter.
LSD: Pretty good for a first time I suppose, but in the average case having less control over precise dosing is a slight drawback. Other than that, it is of course a VERY complete package, an all-round winner. It takes extra care to expose a beginner to this full potential of psychedelia... with milder psychedelics there is a bigger margin to be 'sloppy' and make beginner mistakes as they are easier to control.
LSA-containing seeds like morning glories / hawaiian baby woodrose seeds: They tend to have some side-effects, sometimes heavier than other times... and the psychedelia is in my opinion a bit peculiar and at average doses perhaps a bit limited, but the dreamy state and body high can also be pretty good. There are worse choices for a first psychedelic and these seeds are relatively available for the uninitiated.