The Gamo Whisper is a gimmick. Most of the noise from a springer comes from the spring and piston, not from any type of muzzle blast (unless you get oil in the compression chamber and it detonates or "diesels").
Excluding pre-charged pneumatics (PCP's), you are left with 5 choices.
Spring-piston, gas ram-piston, single pump pneumatics, multi-pump pneumatics, and CO2 powered (CO2 cartridge or bulk fill, as with the AirSoft air guns).
Single pump pneumatics are the most accurate, but will have limited velocities in around the 575-600 fps range with .177 pellets, 7-8.5 gr range. Adequate but not optimal for small varmints, but rabbits are easy enough to dispatch with correct shot placement.
Multipump pneumatics can shoot with as much power as a PCP and are also very accurate, but velocity and therefore, POI will change with the number of pumps. Pumping gets old, though.
Springers probably fit your described purpose best, but don't go for a "magnum" or high power version (and don't believe manufacture's quoted FPS specs either)> Higher power with a springer means 1) harder to cock, 2) more noise, and 3) harder to shoot accurately because of the "bounce" and reverse recoil of the spring power plant. "Tuning" a springer can make them smoother and quieter to shoot.
Gas ram (replacing the spring) air rifles have a shorter lock time, are a bit easier to shoot accurately than a springer (IMO), can stay cocked for long periods without damage to a spring, and typically have good power. They can be tuned to some extent.
Either a springer or a gas ram gun with a wooden stock will be generally quieter than the typical hollow plastic synthetic stock air rifles; the later can be filled with foam to help quieten them down.
In the "4-bill" range, presuming you want the gun scoped and will spend around $100-$150 on scope and mounts, the air rifle I would suggest for you is a Mike Melick tuned B-26, a Chinese clone of the Beeman R9, in either .177 or .22. For your stated purpose, either would be adequate for squirrels, rabbits or birds at 25-35 yards. The .177 will be cheaper to shoot because .177 pellets, per count, are cheaper than .22 pellets.
I think you can reasonably expect 800-825 fps in .177 or 650-675 fps in .22 with 1/2 inch groups at 25 yards. The B26 also has a pretty reasonable clone of the Beeman Rekord trigger -- two stage, adjustable to very light pull weight. Drop Mike an e-mail and tell him what you are looking for. It is always a pleasure to do business with him.
Mike Mellick's contact:
Make sure you get an air gun rated scope; consider this one:
and these mounts: