Most of the variable speed pumps are quiet, put they do cost upwards of $200 and could involve minor or somewhat moderate re-plumbing issues. Not a good thing when dealing with 20+ year old plumbing.
I have no direct experience with variably speed pumps, just what I've read. Reading reviews on Amazon could help but I'm sure something would hit iff'n you did a forum search.
I just installed a small pressure accumulator tank, about 24 oz capacity. This has helped the el cheapo Shurflo(four chamber) that I have to greatly reduce the aggravating cycling noise of the pump.
The tank, while not THE answer to noise, has helped with it and it should help the pump to last longer with the reduced wear on contacts and reducing battery draw as it's not stopping and starting constantly. On medium flow from the kitchen faucet it used to cycle 3-4 times to fill a six ounce cup. Now, it may or may not run but if it does, it runs longer and quieter to fill the pressure tank. I've not used it in the shower yet, but I think it will work well there.
I bought this one:
Not an exact answer but WTH.
I mounted the tank at the inlet for the toilet. I tried under the sink but the 18 year old plumbing was not cooperating and I didn't have room next to the pump without disturbing old plumbing. The threading on the tank is an exact match for the Thetford toilet so I just went to the store and bought a 20" connection hose to run from the tank to the toilet. Easy install, just make sure none of the threads get cross threaded. I pulled my toilet to make sure I had a straight shot at it. Way too easy to cross thread otherwise. Iff'n it hasn't been done for a while, combining a toilet gaskets refresh with the tank install would seem prudent
You also may want to get some extra foam for mounting the pump.