By "Dolphin games", I assume you mean GameCube? GameCube emulation requires a
lot of power (since emulation is necessarily a lot more expensive than using
the original hardware), though I don't know how much, so you won't be able to
slack on it. My brother has some kind of slightly old gaming laptop he got
refurbished, with an Intel Core i7 CPU and some sort of Nvidia card; it
wasn't enough to run GameCube games at full speed (he was playing Super Smash
Bros Melee).
For the GPU, just use Intel integrated graphics. All modern Intel CPUs come
with one. If you find you need something better, you can get an Nvidia card
later (doing your research to make sure it works today if you need it to work
with Linux).
If you need wireless, you will need to watch out for that and try to get one
with an Atheros card supported by Linux-libre. Otherwise, you can just use
ethernet; that usually works without blobs (ethernet will probably be fine
for a desktop PC).
