A HP 54720A or D is a reasonable scope. Plugin modules to 2Ghz, color screen etc. i have one with 54712A and 54721A modules and that's fine for me. $1000Us will buy you a fine specimen thus...
http://www.ebay.com/itm/HP-HEWLETT-PACKARD-MODEL-54720A-OSCILLOSCOPE-W-TWO-54721A-AMPLIFIERS-1159-/401018882278
Yes its big and a little noisy but its exceptionally capable
That's only true for its bandwidth and modularity (which includes optical inputs). As a scope per se, the 54720 is actually pretty basic. Trigger, math and measurement capabilities are somewhat limited for a scope in this class (it does have statistics, though), and processing is painfully slow. FFT on this thing is a real dog even though it only uses a few thousand points.
We had 54720As and Ds when they were current (~1995?), and they were great for the things we needed them to do (TDR, jitter measurements), but as general purpose scopes they weren't great even at those days, especially when considering the input limitations of the various modules. Many people also didn't like the typical HP single knob user interface (also found on the older 545xx Series scopes), although I have to say I did really liked it.
Don't get me wrong, the 54720 can be exceptionally great value for money if you need very high bandwidth, the available optical inputs and the modularity, but outside some niche areas it's not much better than any other digital scope from the early '90s. The same money ($1000 for an untested 54720D) can get you much more versatile scopes that satisfy the 1GHz bandwidth requirement and make better general purpose scopes.
I briefly had a HP scope - it had some good attributes but I think I'm with whoever said "Tektronix for oscilloscopes, HP for everything else" - I'm kind of a Tek scope fan. And a closet Keysight fan. Not to say I wouldn't take a LeCroy or HP or another scope - almost any oscilloscope looks good to me.
The thing with that old saying
"Tektronix for oscilloscopes, HP for everything else" is that it was true when analog scopes were still current, and Tek was without doubt a leader in analog scopes who has pushed technology forward. However, that isn't equally true in regard to digital scopes, in fact Tek has been pretty much a follower when it comes to DSOs, and pushing DSO technology was left to mostly LeCroy and (to some extend) Agilent/Keysight. Plus many of the old Tek's suffered from a capacitor plague, and the UI was pretty horrendous even by those days' standards.
If you want an old digital scope I'd pretty much focus on LeCroy and HP/Agilent.
I don't know if the reason you started this thread is for curiosity or if you're thinking on buying a scope, but if its the latter then you should first get your requirements right (i.e. what you want to do with the scope, why you think you need 1GHz bandwidth etc), then sort out your budget, then find out what it buys you and then do some thorough research (i.e. read the manuals for each scope to get an impression on how they work and what they can do, talk to users that do use one of the scopes for similar things you want to do, find out what the weak points are etc), and then decide based on your findings.