You don't have to, but you'll miss out on about half the available mods. Still, Skyrim Nexus's mods are many and robust (and most of the best mods are there too), so it may be plenty for you.Any reason I shouldn't get the standalone legendary version? I'm a total novice with Steam. I know what it means as a distribution platform, but beyond that, I'm clueless.
I do recommend you get steam, though. It is bar none the best way to get games cheaply for those on a constrained budget, thanks to their biannual huge sales promotions. And there's even a large number of games available for free. At the very least, you should check out Team Fortress 2 (which is free), it'll give you a good introductory idea on how steam "works" while giving you one of the top multiplayer FPSes of all time.