In the sub $100 range you are really limiting your options sad to say. First thing I will say with your winter basement practice in mind that is going to cut out a great many of the spring guns. It does not matter if it has a "normal" old metal spring, or a gas spring, it is still a spring and will shoot on par with the metal siblings. The recoil impulse is very different on a spring gun then ANYTHING else. Not a good practice tool unless is is a sub 700 fps rifle, and going down that far is not going to be ideal for the mammals you want to get rid of.....add to that your price point is going to limit you.
Really I think the best thing in the $100 range is a Crosman 2100 classic. This is basically the same gun as the old 766 from our youth (i am about 10 years behind you) and is actually a very good gun, not a good gun for the price a good shooting gun.....aside from the trigger....they have a horrid trigger.
The thing that will wake up this rifle is the pellets, the pellets sold at wally world are really junk, no other word for it. You need to hit one of the bigger online airgun sellers and get some good JSB, H&N, something along those lines and the gun will be deadly inside of 25 yards.....and NEVER EVER SHOOT A STEEL BB IN THIS RIFLE....more on that later.
Story time:
I bought two Remington Airmaster 77, same thing as the 2100 only black and at the time sold at wally world. I also bought two decks of cards one for each rifle. In my pellet testing I found that the pellets sold at walmart, bass pro, any big box store that sold airguns, these rifles just flat would not shoot straight, in some cases minute of playing card was asking too much at 25 yards.
With good pellets both guns would put 10 rounds into the suit of a 10 of clubs for example, so 10 shots all hitting a club at 25 yards. That is very acceptable. The ammo made all the difference.
Not the pumper, but another air rifle, this is a photo of 10 rounds shot from two different pellets, you can easy tell the difference between what the gun likes and what it does not. Point of aim is the X for the top, and the 8 for the other group, and I think the flyers are me.
The BB thing is, that copper coated BB is steel, and MUCH harder then the barrel on these guns, it will destroy the barrel in short order. If you want it to be accurate don't shoot steel BB's There are lead BB's available, and "non bounce back" type BB's, but never ever steel.
The triggers flat suck, no way around that, you can make them a little better with some universal tricks, but you can't make a silk purse out of a sow's ear. I really wish something higher end pumper had better triggers....and yes I know about the benji's, they are not much better IMHO, and over the posters stated budget.
Pumping is going to suck, no way around that, it is what it is.....look at it as a workout. Leave one pump in it.
Oil, it needs oil, penngun oil is the standard, but really anything that IS NOT dino oil will not be an issue. If it is dino oil the seals will swell up....ever put power steering fluid in a brake master cyl....yea that.
I did my tests to show that these "cheap" guns are actually good guns, I don't have the videos anymore, I should do it again and post them on youtube with a few different camera angles for those that say it is not possible, you never change the mind of those people, even with two guns they will say "you got a good one".
Let me know if I can help.