That's what I'm doing. (Was away for a few days, so couldn't reply to suggestions in this thread - let's see what I can do.)
So look, with record input 1 enabled in my DAW, input 1 on the interface turned all the way down and nothing plugged in, I'm getting noise that averages at -55 to -50 dB, with peaks at -48 dB. The spectrum says that most of it is below 100 Hz (a bump that peaks at zero), with some noise above 100 that's basically flat across the spectrum. When I turn the input up (again, without anything plugged in), the noise above 100 goes up and whole thing peaks at about -42 db.
This is way too much, like I said above, if I have to use an amp sim vst - it's unworkable. Gates suck, etc.
BUT, I answered my own question by doing a further search on thomann. Looks like what I'm looking for is a recorder - such as those two:
https://www.thomann.de/intl/bg/denon_dn_300r_mkii.htm
https://www.thomann.de/intl/bg/tascam_sd_20m.htm
If you guys can recommend any other device - please do. Working out what's the reason for this noise I'm getting is an exercise that I'll do on my own, when I feel like wading through shit like this.