1 Large 12V battery would suffice. Most robots today use LiPo batteries so you would want a 3S (3 Cell) battery with a capacity of ~3000mAh. If you don't like LiPo's, or don't feel comfortable with them yet then a standard 12V NiMH pack would do. they are very heavy compared to LiPo's but don't require specialist chargers and are generally safer than LiPo's.

To control the motors you will need a pair of speed controllers. Hacked TZ85A are all the rage right now and will last you several robots if you treat them right.

Side note - If you put the motors on 24V you would burn them out, which would be bad. Teams do occasionally 'Over Volt' their motors to get more power but by no more than 50% (unless you are feeling very brave). But there would be nothing stopping you from having lots of 12V batteries wired in parallel to make your robot drive for longer.