As long as you get past the major twist in KOTOR, you're pretty much okay to get into the KOTOR II story, as you do hear a couple of story points about KOTOR I that will spoil it if you havn't completed certain parts of the game.
[**** MAJOR SPOILERS IF YOU HAVE NOT COMPLETED ***]
Highlight to read, just to be careful
Well, if you have gotten past the major twist mid-game, you're okay, but if not, here it goes.
Revan was not destroyed as you are led to believe, your character is in fact Revan, just stripped of memory, leaving you to be as powerful, just with the choices of light or dark again.
Key aspects of the Lightside story, (Which is what KOTOR II canon follows on from, not the Dark Side Story):
Bastilla is captured and turned to the dark side by Malak. You then turn her back, and she helps use her battle meditation to help win the large space battle going on for the Republic.
You end up killing Malak, Republic wins!
Key points from the Dark Side choices of the ultra evil:
Bastila turns to the Darkside, when you then encounter her, you persuade her to join you and help you take over the galaxy, not Malak. Half of your party then turn on you, and you have to kill them, those being Jolee Bindo, Juhani, Mission and Zaalbar. Carth then runs off to the republic. Bastila then helps use her battle meditation to aid the Sith to defeat the republic in the space battle. You of course still end up defeating Malak, Sith Wins, you are ruler of the universe etc.
There are also middle side, where you can end up killing Bastila instead of turning her to the light side or joining you as dark side.
That's about it really.
[/**** MAJOR SPOILERS IF YOU HAVE NOT COMPLETED ***]
KOTOR II wise, it's a very good game, just it starts out a little slowly with regards to getting a lightsabre, but you do start as a Jedi straight away. The ending is also a little weak, but that's mainly because the game ended up being rushed out, and the ending cut shorter than intended.
One of the big plus points of KOTOR II is that a lot of your party can be turned to Jedi/Sith with influence based on your actions, so you have to understand what characters will like/dislike based on your actions etc.