There are basically three kinds of wheelchairs:
Power Wheelchairs - A wheelchair with a motor so the user can navigate on their own without being pushed by a caregiver.
Dual Axel Wheelchairs - A wheelchair with a large back wheel that has an attached handrim so the user can propel themselves.
Transport Wheelchairs - A wheelchair with 4 smaller wheels, that is designed to only be pushed by a caregiver.
Wheelchairs are typically referred to as 18", 19", 20" or 22". This is a reference to the seat width.
You will also want to consider the type of arms you need. Desk arms are shorter in length and sometimes fold up and out of the way, making it easier to sit at a desk or table.
Weight capacity, foldability, weight of the wheelchair itself and footrest options should all be taken into consideration.