lol, I just turned 40, so I feel your pain.
400-500 is a decent budget for the systems you are looking to emulate. Normally I would recommend a i5 or better when building a system, but if you are just emulating up to 16bit systems and MAME then you could get away with a i3, I would say 8Gb of ram also. I would also through in a cheap graphics card, this will help if you want to use shaders on the systems you emulate.