The choise of a battery is really a challange!
If you are patient I would recommend a rechargeable Zn-Air battery,
see
www.revolt.com. It has the best energy densities - when it will
become commercially available.
If yo cannot wait, I recommend Li-ion chemistry. It is the power of
modern cell phones and notebook computers. There are special charger
chipss available just for Li-ion batteries, use one of them. You
should connect enough cells in series to get some 6 V of voltage from
the terminals. Using a low dropout linear regulator you can then get
an accurate 5 volts for your Beaglegoard. Li-ion AA size cells come
with capacities well ower 2 Ah so they would power your board for two
hours without charging. And much larger size larger capacity cells are
also available. Just be warned, your cells can easily cost more than
the Beagleboard... As I think of it, a spare notebook Li-ion battery
might just be the easiest solution for you. Get one with the highest
capacity and a nominal voltage no less than 6 V. Then make the
Beagleboard 5 V with a fixed voltage 5 V low dropout linear regulator.
The solar cell should be able to produce say 9 volts and 5 amps so you
can charge some 30 Ah during the day to cover the consumption during
the night with a little of spare electricity. All this will cost you a
nice sum of money!
Good luck for your interesting project!
Keep us informed on your progress,
siñ