I would say get a .30, something you can make really quiet. Most larger big bores are harder to quiet down unless they have a long moderator on them.
Also, I don’t believe there are any available that meet every thing you listed. Quiet, affordable and accurate and big bores don’t really go together. You can get two out of the three maybe.
FloridaBullfrog has a good video on YouTube where he reviews the Texan .30 and tunes it up for slugs and down for pellets. He also takes a doe with that same Texan using a special permit.
AEA seems to be making some decent big bores on the cheap, but I’ve never tried one. I would suggest a Texan SS, an FX Impact in .30 or .357, a AGT Uragan in .30, AAA Slayer or Evol , RAW HMX1000 in .30 but most of these are not really affordable to people just getting into Airguns. The budget for PCP stuff also needs to include a pump and most likely a compressor and tank, plus fill setup.