Even overclocked if emulation of 6th generation (GC generation) or newer is your goal and you want the most compatibility with your collection of games then honestly a CPU with better STP (Single threaded performance) would be a good choice.
If you are willing to buy used a Haswell i5/i7 can possibly be found cheaply and can handle what you want easily. If you would rather only use new parts a Pentium G4560 based system can easily come in around the $400 range (less if you have good parts you can already use.... though your ram would need to be changed to ddr4/ddr3l depending on the motherboard).
Here is a part picker UK (so depending on where you live prices will vary) that Helios likes to post
https://uk.pcpartpicker.com/list/hkYKm8
The nice advantage is that this system will not only handle most of Dolphin 1080P (there are always edge cases), but the nice graphical upgrade a 1050 gives you will easily handle some new PC games (GTA 5, Overwatch, and other).... though it is not a future proof system for New PC gamesand newer games made to push the limits or for what ever console generation comes next will probably start to make this setup show its weaknesses (2cores with hyper threading only, 2GB Vram, to name a couple).
If you are willing to buy used a Haswell i5/i7 can possibly be found cheaply and can handle what you want easily. If you would rather only use new parts a Pentium G4560 based system can easily come in around the $400 range (less if you have good parts you can already use.... though your ram would need to be changed to ddr4/ddr3l depending on the motherboard).
Here is a part picker UK (so depending on where you live prices will vary) that Helios likes to post
https://uk.pcpartpicker.com/list/hkYKm8
The nice advantage is that this system will not only handle most of Dolphin 1080P (there are always edge cases), but the nice graphical upgrade a 1050 gives you will easily handle some new PC games (GTA 5, Overwatch, and other).... though it is not a future proof system for New PC gamesand newer games made to push the limits or for what ever console generation comes next will probably start to make this setup show its weaknesses (2cores with hyper threading only, 2GB Vram, to name a couple).