Yah, start slow. That's the best advice I can give. It does take time and patience. The S2 is what many, many of us started with, so you're in good company!
That chassis has it's "foibles," but has been around long enough to be practically a staple of drift for as long as it has been out. What you see at Youtube is the result of fine adjustment, and a lot of money in option parts. There are a few rules to keep in mind......
Tires are going to be an ongoing expense. Get used to it. If a set doesn't perform to your liking on one surface, save them, and try them on another. Keep doing this until you have a set for every eventuality. This you can effectively pare down to three or four sets, but that's about the least number of sets you would have for all surfaces, because there is no such thing as the "all-purpose" drift tire.
Some surfaces will never be optimum. You can drift and drift and drift, and nothing you do works to your liking, and it may not be you, that's the problem (as discussed above, in another reply). You will learn in time, what works, and what doesn't. Again, patience is your buddy.
Never make more than one adjustment at a time. Every adjustment affects others, so you can easily become confused, if you do too many at one time. Get acquainted with every adjustment on the S2. How it works, how to adjust, and that will help you identify a problem. My advice? There are manuals for certain chassis (mostly race chassis) that have adjustments you can refer to. The S2 will not have all of them, but for the ones they do, you would be best served by downloading a manual, and copying it, and put it in a folder or some such, until which time you become accustomed to each adjustment enough to not need the manual any longer. I suggest the X-Ray T3/T4 manual, and Losi's JRXS Type "R" manual. Any of those are very comprehensive, and tells you what each adjustment is for, and what it does, and how it affects other adjustments. This is true of all chassis that are adjustable.
As for size, the next size down from 1/10th is Mini, or "M" class. "M" class are actually 1/10th scale, and most car bodies you will see in this class, are representations of full-size mini and micro cars, so compared to "standard" 1/10th bodies, are comparable to them in overall size. "M" class 4WD drifters aren't hard to drift, but are "twitchy," so require a little experience. I have one, myself, an ABC Hobby Genetic, set up for Gymkhana (the driving Ken Block does), and it has the strength and size to do the crazy things KB does with his Fiesta, only in "M" class!
But I digress.......Just watch that HPI drift video I referred to, as many times as necessary, until you get the basics down, then move on with harder things. Do circles first, until you can do them near identical to one another, then reverse them. Then move on to figure eights, in both directions as well. Once you accomplish those, you're ready to make a course of your own. It just takes time and patience. You may find that you have outgrown the S2, as we all did, and it's time then, to get something better.