a) Try to spend < $100. Used is fine.
b) 2 Channel scope.
c) Sync Analysis - Highest frequency I know of in retro gaming is 31 kHz horizontal sync, which is great considering modern oscilloscopes measure into the MHz range at all price points.
d) Frequency Response / AC Sweep on a Bode Plot to test LPF - I can't find a used oscilloscope with built-in AC Sweep for < $300. Separate function generators are cheap but have to form a Bode Plot from the oscilloscope in data export myself.
I'm a fan of the vintage 2 Channel Hitachi v-211 and v-212 scopes that have built-in sync separator circuits just for Television Sync! Can be had for $100 but no data export, analog measurements and green screen CRT hell.
Any cheap ish scope that you can recommend? Or do you have a strategy like asking local universities with electrical engineering departments if I can buy one they have sitting around?
Note for those who have never touched an oscilloscope: They use BNC connectors but at 50 Ohm instead of our standard 75 Ohm.