At BatteryShip can I choose what battery chemistry I would like to purchase

Most of the time you can not. Most PDA's and other mobile devices have been designed for one type of battery chemistry. However some models can take either LI ION or NI MH.

More Info:
Here are some of the laptop models which accept both LI ION and NI MH batteries:

Compaq Presario 1200, 1600 and 1800 series

Compaq Armada 1500 series

IBM Thinkpad 390 series

IBM Thinkpad I Series 1700

NEC Versa 2600

NEC Ready Laptops

All other models use one specific battery chemistry and cannot be replaced with the other.