If you do go for an HP8568B then I can give you some info about using one at home:
The HP8568 is a really nice analyser but it is big, very heavy, consumes lots of power and makes lots of fan noise. None of this is a problem in a busy RF lab but get one home and put it in a smallish room (on a trolley?) and suddenly it takes centre stage and the fan noise can be very annoying. The other issue with the 8568 is the CRT is now beginning to become a weak point in terms of reliability. Many lose brightness or focus once the CRT gets tired.
An awful lot of 8568s were bought for use in a rack for automated testing so they sit and run all day every day for many years and this takes its toll on the CRT. You can turn off the CRT in the menus for ATE use to preserve CRT life but I doubt many people cared enough to bother.
However, it is by far the best bang for buck used analyser available if you can live with the issues above. I have one here and I also have the 22GHz HP8566B alongside it. The HP8568 is simply a fabulous piece of engineering and it oozes quality from the moment you switch it on
Note: I'd be VERY wary of fitting an LCD replacement screen. I've seen the specs on one LCD screen that is marketed for the 8568B and it only offers 640 x 480 for the whole screen. This is not good.
By comparison the display in the 8568B has 1000 x 1000 data points 'just' within the 10x10 graticule area. This is pretty awesome and should not be ruined by some shoddy LCD replacement. The LCD will have to do some unwanted and performance sapping scaling to make the 1000 x 1000 data block scale to the graticule area nested within the 'total' 640x480 available so there will be a notable loss in quality on 'moving' data. The CRT display draws the 1000 x 1000 datapoints using vectors and if you look closely at a healthy 8568B CRT then the display quality is wonderful. Sadly, many CRTs are tired and past their best.
So I would advise looking for a HP8568B that has not been hammered in a rack mounted ATE environment. Check the CRT and check the front panel buttons all work (no dead or deaf buttons) and make sure there are no fault reports on the screen and make sure it can pass its automated self cal routine (takes a minute or so for the calibration program to self test and self calibrate and produce an onscreen report)
Also, be prepared to buy a second one as a spares donor becaue it WILL fail at some point due to its age.
Despite the HP8568B being such a fabulous analyser I do think that most casual/hobby users will be much better off with the little Rigol 815 because they won't need or appreciate the difference in RF performance. But they WILL like the small size, the portability, the modern colour display, the modern connectivity, the (useful but rather ropey) tracking generator and the fact that there is already a growing community of 815 users online to offer advice etc.