SkyUI - This is a modification of the User Interface. The UI may be okay for a gaming console but it's poorly designed for a PC which is why SkyUI is possibly the most popular mod available.
Skyrim HD - 2K Textures - This is the most well known comprehensive texture mod, modifying all environmental textures (buildings, terrain, flora, fauna, ater etc.) - much better IMO to the Bethesda High Resolution Texture Pack which is also buggy (when you get Skyrim make sure you uncheck the plugin for it or it will autodownload into your game).
A Quality World Map - With Roads - Exactly what it says, it's a better map to replace the vanilla one.
These are basic ones to start you off which wont conflict with other mods. Always read the mod description and notes before installing a mod. While it's time consuming, I recommend going through the user comments as well. Both can disclose bugs, glitches and mod conflcits which you should know about before using a mod. To install mods I recommend
Nexus Mod Manager. It's the easiest way to install mods if you're not familiar with how to manually install them.
Wrye Bash is also a very important mod manager tool that allows you to monitor your mods for corrupt files and mod conflicts as well as many other things.
BOSS is also a useful tool to optimize the loading order of your mods.