I would definitely suggest a .22 LR, especially for 25 yards.
I love my Henry .22 lever action. It is versatile in the ammo I can use for it. Any velocity long rifle or shorts. Fairly light rifle. Well within your price range. Holds 17 long rifle rounds or 21 shorts. The action is smooth, the gun is accurate. If you enjoy iron sights, I can reliably hit a 1/4"-1/2" target with my Henry .22 at 30 yards with iron sights no problem. Although currently I have a red dot on it, mine is grooved so that an optic can be put on it.
Mine has given me around 12 years of dependable regular use. So many thousands of rounds.
If you prefer a semi automatic, Ruger 10/22 all the way.
A bolt action with a scope will bore you to death at 25 yards. Not saying don't get one, but you need a better range to enjoy it.