I don't think you should worry too much. My gf bought a laptop few years ago for a bit over $600, it's got AMD's dual core 2GHz processor, 4 gigs of ram, and some crappy originally built in graphics card (since PC was's intended to be used for gaming) and I actually run Skyrim on it between mid and high settings (though without the grass), and I don't really use graphics mods but I do have HD wwater texture replacer and there aren't any fps drops.
Also, to actually answer the questions. You do have to use Steam, but it's easy to use, when you install Skyrim it'll install Steam for you and all you gotta do is make an account for it as if you're making an account for Facebook, Myspace or anything like that (it those would have to be installed on your PC). Also note that Steam is to be used online, so when you're playing Skyrim you're basically streaming part of info over to your account. But Steam can be set to work offline.
Mods are copletely optional and you don't have to use them, ever. Many mods are on Steam Workshop, but Skyrim Nexus is much more known and used site. Complexity of installing mods depends greatly on what the mod does. It goes from simple texture replacers where you just copy the files over to your Skyrim directory (not even if you use Nexus Mod Manager, software that helps you install mods with ease), from mods that require a whole separate software installed 1st in order to add support for some new features, and then installing the mod itself after which you then need to set it up over added option in the game's UI etc.