Okay, there are a couple of battery ideas. I'll try to give you a brief overview.
You have, alkaline, NiMH and NiCD, Li-ion and Li-poly.
Basically, in that order, you have cheapest to most expensive. As for quality you can pretty much use that order too. Things to take into account are battery life (Li-poly being the longest lived), cost (Li-poly being the highest cost), and number of recharges before it becomes pretty useless (once again Li-poly is the best). I'm sure you can research this on the internet using your preferred search engine! Find the right one for you!
I would, on the other hand, try using a super capacitor. In a nutshell, these capacitors are capable of storing a huge amount of charge, without loosing their charge carrying capacity. For example, a Li-poly battery will live for around 1000 charge cycles, whereas a super cap will live for well over 500,000 charge cycles, with no max charge loss!
I suggest you look these up too, as they are probably just as good for what you want to use them for as batteries, but the circuit design might be a little more complicated. And they are about $30 as compared with a Li-ion pack, for about $10
As for power drain, it depends on how you connect them (series, parallel, or combination of both) Either way, you will have lots of volts and little current, or lots of current and little volts. I think, depending on colour, that you will need at least 1.5 - 3v before the LED comes on, but only 15mA current draw. So for 10 LEDs in series, you could be using as much as 15-30V to push through. Much better to have say 4 parallel lines, of between 2-5 LED's.
That way you only need to supply 3-7.5V and 60mA which is right in the range of a Li-ion battery pack!
For a 1700mAh 7v battery you can get roughly 28 hours out of your light before you need to recharge. Might not even need the dynamo
Also, If i have got any of this wrong, someone please tell me
Hope it helps!