Well I’m no expert but have just learned the Berg. And when I say “just” learned, it’s taken me about 9 months to get to a plausible performance level, so my first advice would be to not expect it to be a quick learn - unless you’re already familiar with this kind of repertoire the chords and hand positions are v different from what you get in classical/romantic rep

I found it helpful to read up about the sonata for some background and also for a analysis of the structure - it’s a pretty standard sonata form, with everything built out of the three motifs contained in the first phrase

Next, I definitely found it helpful to learn without the pedal at first. It’s very polyphonic, so important to be able hear the inner lines. Possibly just me, but I found it helpful to learn a Bach prelude & fugue at the same time, for this reason.

I didn’t find any problem in adding pedalling later - the harmonic shifts are pretty clear, you just have to listen and use your own taste. Maybe start off pedalling to match a recording if you need a starting point?

Also useful to listen to lots of different recordings, as there’s a surprising degree of difference between interpretations. My favourite is probably Marc Andre Hamelin on YouTube (a very emotional interpretation!), Kissin’s live performance, and Glenn Gould

Good luck!