When the computers and video games that you are talking about were designed, 2 channel scopes were the norm in design labs. 4 channel scopes were very expensive (eg. Tek mainframes). People also knew how to use the external trigger input on 2 channel scopes when necessary. That's not to say that a 4 channel scope isn't highly desireable, but it's not an essential. This might make your limited budget stretch further.
Another item that was very expensive back then was the Logic Analyser. These day, you can get a basic Saleae USB logic analyser clone (which works with open source Sigrok) for <$10 for the 8 bit version. Back when everything was external to the microprocessor, wider LAs were used, typically 24 bits or so. 16 bit Saleae clones or even 32 bit USB models are also pretty cheap now. The work methodology was scope to look at signal integrity/quality, setup and hold timings etc, and the LA for decoding busses and decodes. SPI, I2C etc, weren't a thing back then, so protocol decoding is less useful.
I would factor both into your budget, that might mean spending a little less on the scope, but I think you will find the combination helpful.