What exactly are you planning on doing with those games and consoles? A good soldering station will run you about $100. Hakko FX888 is pretty much what everyone is going to recommend, not my cup-o-tea but it's the standard starter station.
If you're planning on doing component level repair, you'll need a good quality DMM. I know a lot of people complain about Flukes pricing but the speed of the continuity beeper is a must have and most other brands just don't have that. A Fluke 115 would be fine for you but you might be able to find a used Fluke for a reasonable price...they pretty much stay accurate forever. I have techs at my shop that have 25+ year old Flukes that haven't been re-calibrated that are still accurate.
If you're on a budget, HF mini pliers will work and their micro flush cutters are actually really sharp. I use mostly Knipex, Xcelite, PB Swiss and Felo for my hand tools but it's a luxury not a necessity.
Also, if you're going to be disassembling items like that you will need security bit sets. Don't fall for the ifixit bandwagon, they will work but they are overpriced Chinese bits that just aren't very good. You probably won't use these enough to buy an expensive kit but a nice set of precision phillips/slotted screwdrivers are a must, I like Felo. Make sure the precision kit you buy has PH0, PH00 and PH000...a lot have just the PH1 and PH0.
Good flux core solder and good solder wick are must-haves. Some form of third hand is extremely useful. I built one out of copper wire and alligator clips with a recycled TV stand base. My next version will be with coolant hose similar to this: