Welcome aboard, mate. There's a lot to like about PC gaming; better graphics, mods, better reliability, and cheaper prices. There's also a few genres you don't get on console, and a bunch of really superb games for under ten quid.
So, Skyrim is my main area of knowledge so I'll let others fill you in about the others.
First and foremost, the non-negotiable MUST INSTALL gameplay essentials. First you're going to want to get SKSE. SKSE just lets you run much more complex mods, it's a heavensend because it allows you to add all sorts of really complex goodies. Second, NMM(Nexus Mod Manager) Free-to-use App made by the Nexus, makes installing/managing mods a snap. No reason not to use it, since it makes installing a mod a two-click process. Thirdly, you'll probably want Werne's 72 hours Respawn mod. Skyrim enemies DO NOT RESPAWN when killed. Well, they do, but it takes about a month of gameplay real-time. Werne's mod shortens that to about 72 hours in game, ensuring that like Oblivion, you'll always have some baddies to fight and stuff to loot.
Second? Pretty Face and Enhanced Character Edit. When these two are installed together, you get an entirely superior character customisation screen. I can't really state enough just how superior, either. It's just in a different league. Dozens more sliders, numbers on the sliders, the ability to apply an NPC's face morph to yours, the ability to customise NPCs, the list just goes on and on. It's a must-have. Plus, it even adds better character graphics.
Third? All the Unofficial Patch mods you can find. They make a big difference to reliability and playability. A big difference.
Fourth? On the general topic of better, more reliable, the Amidianborn Book Of Silence mod is a must for anyone who's computer cna handle it. Replaces a lot of data mostly regarding armour, vastly enhancing the graphics and artwork without changing the actual cut. Some of the enhanced armours, particularly the Elven and Ebony sets, are actually prettier than the fully mod-added gear. Still has the same shape and cut as stock armour, but the graphics and colours are much improved-texture detail is something like six times higher.
Fifth? Any of your choice of body/face mods. Choose wisely, you can essentially use these to choose the 'art style' of your character, from classic fantasy to... vaguely realistic. Your character should be something totally within your control; you're in charge of their story, and you may as well have similar control over how they look.