As Mahendra's answer indicates just about all of the commercial smart bands use Li-something based batteries.
However if this is for a class project I'd recommend using something like a CR2032. If you buy a bulk pack then they are relatively cheap and hold about 200mAh each.
For testing and development you can easily replace the battery holder with a wired connection to two AA batteries to prevent burning through too many batteries.
Your end product won't be rechargeable but as a class project you probably don't want to spend half of your time designing battery charging and monitoring circuits.