Rohan The Wind Waker wrote:
Well most of all people start with a NES. Pretty simple and cost like $120 if you have nothing. I right now could start one for $60. $60 for the screen. But if you want to have more of a chalenge start with a Gamecube (Not recomended for NooBs. I went through 3 boards all ready in 2 days. )
The thing with gamecubes is that they're pretty much the cheapest system out there at this point. If you go wall power and cheap screen, you can easily have a complete portable for under $100:
$25-50: LCD Screen
If you want battery power, you need to either get a screen with built-in battery & charging circuit, which simplifies the amount of work you have to do but also limits you to the batteries that the oem put in, or get your own batteries/chargers. If you go anything under 11.1V batteries, you will need to do a custom power supply (free with samples from TI, otherwise around $30).
As for the actual modding of the gamecube, as long as you are careful, take things slow, and follow the guides found online, you will probably be fine. Hacking/modding depends largely on your patience and diligence, as well as having some knowledge of how electricity works.