What is your preferred least expensive but reliable used-market scope that has at least 1 GHz of bandwidth?
It depends on what you want to do, really. 1GHz bandwidth is pretty meaningless if the other specs aren't adequate for the task at hand.
If usability was at least somewhat important then I'd say a LeCroy 9370/9374 or 9384, simply because while they are old and ugly, they offer very decent specs (1GSa/s to 4GSa/s real-time sample rates, 50k to 8M sample memory per channel), and for a few bucks can have all their advanced options enabled.
On the other side quite often the successors LeCroy LC574 (4GSa/s) or LC584 (8GSa/s) can be found for the same price as a 9300 Series scope. The LC offers faster processing and color screen, and like with the 9300 Series these scopes can have all their software options unlocked for a few bucks, too.
Both are pretty reliable scopes for which Service Manuals including schematics are available, and especially with the advanced options enabled they can still do lots of things that even today can only be found in high end scopes. In this age and (2nd hand) price class there's unlikely to be anything more powerful. Although their age does start to show (i.e. screen burn), and it can take some time to get a good deal amongst all the ebay sellers asking insane prices for their "untested" (yeah, right) gear. But that's a general problem.
However, if money and price was of upmost importance, and usability played no role, then one can save a few bucks by getting one of the antique sampling scopes from the late 80's. They are huge, slow, loud, suck lots of power, and are only really useful for a very limited set of tasks, and due to their age and sensitive components may require a lot of babying, but these days at least they're often dirt cheap.