The Rigol
DS1104Z-S Plus is 100mhz, 4 channels, and has an optional
Logic Analyzer expansion available. They can be had for around $700 USD, which is well within your budget. If you buy the Logic Analyzer add-on, you're still only looking at around $900.00.
If you wanted to spend a small amount more, you could buy the low end of the Rigol MSO5000 series, a
MSO5104 which is a 100mhz model, and hack it to unlock the same capabilities as the high-end model. There's a thread
here on the forum somewhere about hacking the MSO5000 series scopes. And as an MSO, (Mixed Signal Oscilloscope) you get Logic Analyzer capability "out of the box".
From a logic analysis perspective, either of those would be more than capable enough to handle anything that I think generally falls under the rubric of "retro computing". For that matter though, you can probably do anything retro computing related you want to do with a $10 chinese made USB Logic Analzyer and Sigrock. For debugging deep internals of an actual modern PC, you would probably need a high specialized, and very expensive, piece of dedicated gear. Like, if you wanted to view changes on a DDR4 bus in real-time. That's a whole new ballgame.
In either case, don't forget about the various discounts that are available to EEVBlog forum members. Tequipment.net is one of the vendors who
offers a discount. There is also a
discount on Saelig kit. I think there may be others as well.