What you build as base is up to you. I generally build underground or in a cliff face, but have built on a mountaintop and in a ravine on occasion and am currently doing a feudal type castle above ground in a savanna.
As for biomes, it's easier if you chose one with trees and naturally occuring wildlife. Desert or arctic are probably hardest and small island is hard also but less so. Dark forests are a bit of a challenge as there are too many resources there and they get in the way.
I'm not really the best person to answer since I tend to just dig into the nearest hill but if I was going to get around to putting more effort into it I like the idea of digging it into the side of a mountain or mesa, about halfway up with big windows and a big balcony outside.
I've seen pictures of very nice underwater bases with glass domes and tubes connecting them together.
The side of a hill is the best place to start. Especially if you are on hard mode. If you don't have sheep handy to make a bed, this also gives you something to do at night because you can mine resources while waiting for the sun to come up. Don't forget to find a food source soon (plant some wheat or cut down some oak trees for apple drops). Also, once you get the survival stuff going and have time and resources to make things pretty, don't under estimate the necessity of good lighting. Later, you can build out from your hill or convert it into your mine.