The .25 Hatsan you suggest would, I'm sure, perform the task admirably.
Having said that, any calibre would do the job, so maybe a .22? Thinking larger pellet choice and cheaper ammo......22 Hobbies are awesome on rats and cheap.
The .22 is more efficient, so you'd have a sweeter firing cycle for comparable muzzle energy figures.
As most ratting is conducted at shorter range, you really do have a big choice of rifles to go at; anything upwards of 8ft.lbs will be more than ample. Most of the Hatsans offer excellent value for money.
Must admit, this is one scenario where the stumpy little, quick handling Lightning would come into its own, though your stated budget would be pointing you towards a used one.
After all is said and done, though, if you're just fancying a .25 for the hell of it and some extra variety, go right ahead.