Batteries?

[Preparation H67]

I am new to this and I would like to make a portable but I need to know how you figure out which rechargeable batteries to use such as which voltage, amp, and how long it will power the system as well as how you connect them. I want to eventually make one of those Wii laptops but will start with something more with in my skill range with something cheaper that i wont kill myself over if i somehow destroy it. I would like to be able to play while its charging and I would like to knoe if its ok to keep it on a wall plug forand extended period of time (like if i was using outputs to connect to a tv)

I apologize if the question is to general but I pretty much need to know a lot bout the subject and I will probably use NiCd or the other Ni something ones batteries because fro what I have already read they are more nood freindly and you have less risks than li ion ones