Yes, the .177 is enough for those fuzzy tailed vermin.

I like the .25 for its ability to harass all the vermin i encounter.

When i was looking for a break-barrel i was scouring the comments for "quiet enough to take a second shot". The pneumatic cylinder ones seem quieter than the spring actuated ones. I was never able to sound them out in the store so i could never choose based on what i heard.

Sorry, i do not have a specific recommendation