I have a 4-channel oscilloscope and a 34-channel logic analyzer that I use for chip/bus timing analysis, clock frequency, etc. With the speeds of these older systems, you do not need to spend too much money on these. I think I spent less than $500 for the pair, but you could probably do better on ebay.
Just make sure you have at least 10 samples per clock of the fastest component, more is better. So, a 2600 would require a minimum 36MS/s. An NES would require 220MS/s. A Sega Genesis would require 54MS/s. I'm working on hardware emulation of older chips right now where I have 8 operations on the new hardware to emulate 1 operation on the old hardware, so I analyzed the bus at 8 samples per clock to get the most accurate timing that I could recreate.
You can probably find timing charts to help, but nothing beats seeing the systems tick. I've also pulled chips and built basic systems around them to run at 2Hz.