You will likely see a lot of mention of the 4l65e in your searches. Which, in essence, is the same transmission with strengthened components and some additional friction in the 3-4 clutch. A lot of places rebuilding the 4l60e go ahead and swap the parts out for internals of the 4l65e. Which, it does sound like your 3-4 clutch pack is starting to go, it's slipping when you step on it.
The one incompatibility between the two from GM is the input shaft, which requires a different torque converter. Just something to keep in mind when browsing. You might need one if you decide to swap the whole trans at once. Sometimes they come with them, you'd just want to make sure it shows compatibility.
Realistically, you'd just have to find a rebuilder in your area and see how much they'd want (starting) to rebuild it. You can search 'precision transmission 4l60e' on youtube to watch it being torn down. You're mostly after replacing all the little clutch disks, but there's some other wear they may find and want to replace.
If you cant find a good rebuilder nearby, id find a good shop to work with and have them look into a replacement trans from jasper and see how much they're looking for. I personally wouldn't bother with a junkyard part, the 3-4 clutch is the natural thing to go out for most people if it's taken care of. There are some performance rebuilders as well if you wanted to change something about how it performs (shift feel, clutch aggression, built to withstand more power, ect) that arent all that much more expensive as well.
Whatever you go with, check the warranty terms. Jasper is pretty well known thanks to their larger network with smaller shops and they are nationwide.
Just some extra options for you