On the general subject of size, a modern DSO is way shallower than a CRT analogue scope, and lighter too,but the front panel dimensions of my DS1102Z-E are almost exactly the same as my old Tek 475A analogue. Size can mean different things in different situations.
Would you recommend the DS1102Z-E?
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Getting back on topic...
Would I recommend the DS1102Z-E? For me - yes, for you - I don't know. I'd been thinking of a desktop DSO for a while and bought it because it was on offer on Amazon for £235, probably the second most amount I've spent on an item of TE. For me, the reason was a nice deep buffer for capturing and looking at infrequent events. Siglents are reputed to be easier to drive, but it's intuitive enough for me, I've got used to loads of different scopes over the decades so the cost difference wasn't worth it
for me. It's good and solidly constructed and does everything I want. If you want to look at Dave's review and teardown videos, it's simply the DS1054Z but with two channels and an ext trigger rather than four and has all the options factory enabled. One thing I have found to be a surprising source of irritation is the need to transfer screen captures to the PC via memory stick rather than just clicking the save button on a USB scope, I wasn't expecting that to bug me so much. I'm not going to go to the hassle of networking or USB hosting though, I'm running Linux anyway and the Rigol app doesn't support that.
I don't subscribe to Dave's 'beginner entry level scope' mindset or the 'why do they still make 2 channel scopes' (because you can buy them cheaper!). I buy tools to do the jobs that I want to do. I've had a decent high bandwidth Tek analogue scope for nearly 40 years, which is still good for RF stuff.
I bought a 16 bit Picoscope ADC216 20 years ago, literally just before they discontinued them and shamed/conned Pico into giving me one of their last remaining USB parallel adaptors. I added a USB isolator and linear regulated PSU to get rid of the very small residual 50Hz harmonics and with it's low 333kS/s sample rate it is as quiet as the grave for low distortion, low noise audio. That was probably my most expensive TE purchase ever. I need to run it in an XP 32bit virtual machine but that's fine.
Other than that, in 2015 I bought one of the first VDS1022I isolated USB scopes and I think I did the first ever teardown, which sort of became the master thread (
https://www.eevblog.com/forum/testgear/owon-vds1022i-quick-teardown-(versus-the-hantek-6022be)/ ). It's a handy little, easy to drive, 25MHz 100MS/s scope that is still available and does most things well, especially with the alternative S/W that's available. The only shortcoming is the small 4k buffer and no protocol decoders but that's not an issue unless you want to capture infrequent events.
The number of bits you need depends on what you are doing with these audio amps. If you were planning design and upgrades then number of bits would be more important for distortion analysis. If you just want to see how far the signal is getting and whether it's basically the right shape then 8 bit is probably fine and the simpler to drive, the better. Even for audio bandwidth, it is good to have a scope that goes to a few MHz to look for oscillations. As for a signal generator, I don't have an AWG or MSO or whatever, just a nice second hand analogue very low distortion Topward signal generator and a Function generator to go with my 16 bit Pico. I don't need some fancy box with a big LCD display, encoders and keypads that looks like a scope itself to produce a 1kHz or 10kHz sinewave (likewise power supplies). Keep an eye on ebay and make sure you can get a service manual.
Only you know what you are going to do in future. If you're going to get into micros, higher speed logic etc. then facto those in now. If your ambitions don't go any further than repairing basic audio gear, then my attitude is buy the tools to do that job and divide your budget accordingly.