I want to buy a microphone stand to record what's coming out of my amp. But, I would also want to use it for vocals in a band.

What would be a good mic stand height to be acceptable for both? because I would want to mic to be really close to the amp... and the singer to be comfortable enough to sing using this stand.

Just any standard size, you'll be able to point the boom arm up or down depending on the purpose.
There is poetry in despair.
My crappy Stagg one doesn't have a fixed boom.

Not sure I would reccomend it though...the lowest knob broke off in my hand, but I dont really care about that one.
There is poetry in despair.
I have one of those $20 (now $25) Nady mic and stand combos. They say the boom is fixed but mine adjusts. It is a light duty stand for sure. But it works for what I do. I also just got one of those double stands off of Ebay. They have a center mount and a boom. Again cheap and light duty but for $20 and change...

If you want heavy duty get Atlas.

I got a mic stand with a cheap mic pack when I started using mics about a year ago and really enjoy the stand that came in this pack:

I will probably end up buying 3 more stands and selling off the cheap mics on ebay along with the cheap clips. The stands have worked great for me and they have the 3 way adjustment.