How about a crossman 1077.
Have you ruled-out co2 guns? If not, the QB-78 / AR2078 rifles are great guns and the price is way inside your budget.
A Disco with a LDC is very good
A tuned MM b26 is also good, or a used R7/R9.
Might consider a Benjamin trail NP with an aftermarket trigger blade.Either that or the crosman titan, or NPSS.
Well, you sort of can't have it both ways.
The Stoeger and Remington will make some noise.
Cometa 220 Compact
If you don't want to spend the money on an R7, take a look at the HW30s
The X20S is not much quieter, according to one of the online reviews.
Can you practice at 10 yards indoors? I live in a small condo, but even I can get 10 yards with a little effort. 10 yards at small targets is good practice for 30 yards at larger targets. It's just that the pellet trajectory and trigger pull changes a bit with more pumps.
A good affordable bet would be a Crosman 2100 Classic or Daisy 880. They will be as loud as the 953 if you pump them the minimum of 3 times, but when you go out hunting small game, you have the option of pumping them 10 times. They're easier to mount scopes on than the nicer and more powerful Benjamin pumpers. They'll only be powerful enough for up to rabbit-sized game. Is that OK? If these end up being too loud for back-yard shooting, you're not out much money, and you'd still have the option of shooting them indoors.