1. Really this can vary from mod to mod. Some mods such as ones that overhaul the landscape will require you to go into an empty room (such as your house) and then load the mod, or else it will crash on load. Just be sure to read the readme before you install and you should be fine. That being said though, be sure to do the same with any other characters you may have that you may want to go back to... Otherwise you may never be able to play as them again... I know from experience... Not a day goes by I don't miss that guy *sniff*.. anyway where was I? Oh yes, golden rule is, read before you mod.
2. There are so many good mods out there I can't list em all here. Will say though, I have had a lot of fun with Unecessary violence and Deadly Reflex's add a lot to the game, and make playing as a stealth character a lot more fun and rewarding if your into that, and if not still add a lot. Just never been able to get the damned dual wielding to work... Other then that though, I would say go to the Oblivion Nexus, and check out their top 100 list, be sure to check out the ones that interest you, if you like what you see, try it out. Just remember, if you don't like it, you can always uninstall it. A mod manager is a plus unless you really want to put some work in dealing with load order, uninstallation and a lot of other things so definitely get the oblivion mod manager.
Happy Modding!