To add in, some context from the books will also help you as two characters who are only mentioned become prominent characters in the third game, and are very much major characters in the books.
Yennefer of Venderberg is a sorceress who had a chance encounter with Geralt and they hit it off to a degree. Her trying to tame a geenie went not great, but they managed to deal with it with the help of Geralt who made a wish, something along the lines of them not being apart, so they become magically bound to eachother. The start of a pretty chaotic romantic relationship, this is his main love interest through out the novels. He did not remember her due to amnesia til the end of the second game.
Ciri of Cintra is the princess to the fallen nation of Cintra. She was taken by Geralt when the nation as his reward for a witcher contract he did years before, the so called Law of Surprise which is how Witchers grow their numbers. She has the Elder Blood which means she is a descendant of some important elf and is very magically potent and with a great destiny. She is the adoptive daughter of Geralt and Yennefer.
Also for the variation of endings from the second game, look at http://witcher.wikia.com/wiki/The_Witcher_2_ending