Floppy drives are going to be common even in more modern equipment, I've got a WavePro 7200 made in 2005 that still has one in the front panel. I believe it would be a software option for analysis on that unit, but it's got a 2GHz frontend and sample rate to spare.
Something like a wavepro 960 or newer, or a DDA-260 or newer would be some of the cheapest used scopes on the LeCroy side of things. Haven't really looked into the price of Tektronix or Keysight, but I'd assume theirs are comparable if not a little higher.
If you're just looking for an eye diagram, even a base scope of that performance will do the job, but if you're looking for protocol specific USB stuff or jitter analysis or whatnot, that's going to require a software option which is going to be expensive, so I'd look for it as a primary element in a used scope just because it will easily be $1000 or more to add in to one without it.
Also consider the cost and availability of probes. If you're looking for something that will be good for the full bandwidth, you're easily looking at several hundred dollars per active probe, and sometimes more for a differential probe. I think tek probes have the most used availability, but again you'd probably need to used if you're keeping the cost down, a new few GHz range active probe could easily cost as much as a nice used scope...
If no floppy is a requirement, that probably leaves out any Windows 2000/XP based scope and most of the cheapest options for that sort of bandwidth, I'd expect that requirement to cost you at least $1000 on the used market, though of course you're getting a more modern scope out of it.