Depends on the artist many times. For singers I usually want at least 2 of everything, 3 helps. So if we're doing harmonies I'd want two of each. That's four. Ad libs take up 1 or two. If we have more harmonies or other parts 8 to 10. There can be small fills here and there that can take up tracks also. Might just be a short vocal take. It really depends.
Rappers are usually less but 3 or 4 is usually what it ends up being for 1 part. Depends on what the artist is doing could end up being just as in the singer scenario but instead of 2 of each there's just seprate stacks for separate parts. Well, same thing does for singers.
I don't usually have a preset amount of takes I'll need ahead of time. I let the artist do what they want and if it's my call I'll ask for additional takes of parts if I feel I can use them later on. I don't feel that I have to have a certain amount of parts for the chorus if a verse has a certain amount of parts. It really depends a lot on the artst.
I worked with a singer recently and while she had a very nice voice she couldn't nail some of the higher registers that I wanted. I did do about 4 layers of stacato takes, just to accent some words and after I ended up doing a harmony in a part or two by pitching some of the extra takes I took. I don't like to use the same take on two tracks even if I'm pitching/processing one so I took 4 of the same so I could have two to do whatever I wanted. I had the stacks, and had 1 take for additional things she wanted to throw on to. The part was actually pretty simple, it probably sounds like more than it is.
Some singers I just need a few takes for, no harmonies, very plain. I believe I worked on a track recently where I had 3 takes of the same part but might have only used to. Just sounded better without creating a harmony.
Don't worry about how many takes. Just use what you need. More is always better than less. If you can get more good takes, get more good takes if they'll allow you more flexibility down the lines. You might just get two takes that sound good period and if that's all you think you need, that's fine. If 1 takes is all that's needed, that's fine also. It really depends.