^definitely chug the syrup, 300mg at once for best effects IMO. That stuff is so gross that once you get a taste for it, it'll be harder to put down, so down at once, open throat wide like shotgunning beer lol. You shouldn't be disappointed with 300mg at once, it's not intense but you'll be fucked up for sure.
There's probably an equal chance of throwing up the capsules or the syrup, the capsules are big and get stuck in your throat. I've done 600-900mg with those and it sucks.
if you stagger you're going to get different effects. Do you want more DXM (serotonin type effects, psychedelic) or DXO (dissociative)?
What you need to avoid nausea:
1) Ginger extract in capsule or chewable form
2) diphenhydramine 50mg (makes the trip better as well, just don't take more than that), also helps to avoid histamine reactions
3) cannabis, 300mg is boring on its own, first trip or not, this will also help with the nausea
even after all that you still may puke but i doubt it, dxm is pretty nauseating, even as a pure powder. Definitely double check the syrup to make sure DXM is the only active ingredient. Even so all that syrup is probably going to give you the shits, consider immodium as another precaution to avoid the side effects.
Then after 2-3 hours, you've probably come up fully and aren't sick; feel free to drink a couple beers, there's really no harm and many people prefer it. If you drink before, you'll probably throw it up unless you have a strong stomach.
Lastly, enjoy, DXM is one of my favourite experiences, though i grew out of it, i'll never forget it. 300mg is definitely enough to get you high out of your mind, add cannabis and you'll be shocked that you can actually get that high. Then imagine a dose at third/fourth plateau
also make sure you aren't one of those people who lacks the enzyme cyp2d6, i'm sure you'd know by now but something like 5-10% of people lack this enzyme and DXM isn't broken down and you'll get extremely high from 300mg, like way too high. If you've ever had a cough and used dxm at 30-60mg, and didn't have any adverse effects then you're almost certainly in the clear for that issue.