If you don't plan to play more demanding games or play at higher resolutions something like a mobile 3rd gen i3 and its integrated HD Graphics with 2 sticks of RAM are barely enough to play your games in 720p. However I'd still recommend you to get something better. A desktop 2nd gen Intel Core i3 should be enough. A new Intel Pentium G4600 is more than enough but you can use its iGPU.
Don't go out and buy something like a Radeon R5 230. For new cards I'd recommend you a Nvidia Geforce GT 1030. If you want to save money by buying used components get at least an AMD Radeon HD 7770 or a Nvidia Geforce GTX 650. They're cheap on the used market and they're good for emulating GameCube and Wii games.
For storage I'd recommend you a SSD for the OS and a mechanical Hard Drive for your games. If you don't use Windows 10 you could leave out the SSD. I don't know how much storage you'll need. So I can't recommend specific models.
And for RAM just go with 8GB (Or even 4GB if the prices are too high for you)
If you can find a cheap PC with a 2nd Gen i3 or better and it only has an iGPU just buy a good graphics card (in some cases you'd also have to buy a new power supply). And please avoid any small form factor PCs as they can't be easily upgraded if they're upgradable at all.
Don't go out and buy something like a Radeon R5 230. For new cards I'd recommend you a Nvidia Geforce GT 1030. If you want to save money by buying used components get at least an AMD Radeon HD 7770 or a Nvidia Geforce GTX 650. They're cheap on the used market and they're good for emulating GameCube and Wii games.
For storage I'd recommend you a SSD for the OS and a mechanical Hard Drive for your games. If you don't use Windows 10 you could leave out the SSD. I don't know how much storage you'll need. So I can't recommend specific models.
And for RAM just go with 8GB (Or even 4GB if the prices are too high for you)
If you can find a cheap PC with a 2nd Gen i3 or better and it only has an iGPU just buy a good graphics card (in some cases you'd also have to buy a new power supply). And please avoid any small form factor PCs as they can't be easily upgraded if they're upgradable at all.