Bullpup choice. Maybe Impact Compact.

There are some naysayers screaming caliber doesn’t matter. I’ve shot a lot of squirrels with .177 (12 FPE) head shots and they bounce around kicking & flailing. It takes some patience for them to stop moving around enough to put a hole in the skull. I tried a .177 chest shot and it ran away to die somewhere else out of visual range before I could reload. A couple times, .22 polymag flying out the muzzle around 750fps and impacting a bushy-tailed rodent head 15 meters away popped an eyeball hanging out of the socket but the dang thing would crawl around trying to hide. There have been several super-squirrels I’ve shot in the head and still have deliberate movement, then coninue to survive multiple follow-up shots in the head and chest. I know they weren’t misses because the body part being shot would get knocked, then I would see all the holes after recovering the pest. Most .22 polymag shots to the chest would cause blood oozing out as they cling to the tree for a few seconds and drop without all the flailing. BUT, a .25, a polymag chest shot (typically 15 meters) would drop them immediately with a startling “p0p”. Sometimes it was a gory scene with a lot of blood falling from the tree all at once instead of pouring out like the .22. I forget what velocity my .25’s are, but not very fast because I cranked the hammer tension lower until the shots were quiet with pesting accuracy at close range. Sure, it might be dead the millisecond it caught .177 lead in the brain, but if you don’t want all that flailing around, going with a bigger caliber high in the chest might be the ticket.





The good old saying is there is not replacement for displacement. Of course .25 is better, heck, go straight to .30! LOL



BUT it does depend on pellets too, like you said polymag and hades do a number on critters so you don't really need massive pellet to drop them dead. I've done vital shot with .177 hades and they don't run more than a 10 feet. Even the lowly 7.4 crosman pointed pellet can drop a squirrel right there if the placement is right and I've done it many times, I prefer the challenge of a good head shot vs brut force of .25 which is feels more like extermination than hunting. However I'm shooting urban squirrel which most of the time would sit in my tree and star at me while a pellet is moving towards it's forehead.



Only way to drop them DRT is an accurate shot to the neck and sever the spine but that's a harder shot than the brain shot. However shoot whatever floats your boat, no point arguing about what you want to shoot on the internet. As long as the squirrel is dead then it's dead! 
 
I may be crazy but the .25 Wildcat has been calling my name recently.

You’re not crazy. I LOVE. My wildcat mk2 in .25. Very nice hunting bull pup. Lightweight for woods walking, and shoulders easily. Extremely accurate. If I was the OP, I’d look into the wildcat mk3 (compact for woods walking, sniper for long shots) and never look back. Easily tune able with externally adjusted reg, and hammer tension power wheel. Hi cap magazines, and the lightest of the current lineup of bull pups. Paired with the awesome customer service fx offers, and it’s a no brainer. 
 
@vaplinker Of all the FX guns, I consider the Wildcat the best of the bunch other than the Crown if you want a gun for hunting, and I mean hunting not sniping. For hunting, and bush craft I think the Impact is way over rated, and is more meant to be a sniping and bench gun, not a bush crafting gun.

If FX could make a consistently reliable .177 barrel I would consider the Wildcat MKIII, but based off friend's input and their correspondence with @FX and @FXUSA all FX 177 / 4.5 mm barrels seem hit or miss and FX say "just deal with it" or buy a new one and try again.
 
Great choice. My wc mk2 with the 600mm barrel is fantastic for woods walking, so I believe the compact would be even better. At some point I’ll get the compact, but I think I’ll get a mk2 compact strictly for the ease of keeping magazines loaded all the time, and quick to grab and go without having to touch any settings or loading mags (I worry leaving spring indexing mags loaded all the time isn’t good for them). Good luck with your choice, and happy hunting!
 
Any gun I mention I have owned and shot. Sold an Impact. Didn't like how persnickety it was. Had a Lelya 2.0. Probably the best most comfortable gun I have owned. I think I got a semi-lemon and had continuous problems with it and sold it. Accurate and durable as can be. I too am taken by compact bullpups. I have a .25 taipan shorty. zero problems. A daystate .22 and even though it's sold as a bullpup it weighs more than my other three rifles combined. But, the electronic adjustability, not mechanical, is amazing. I now use it a .25 yds on low power and the shot count and accuracy is there. The RTI Prophet in .25 is simple, reliable, and accurate...winning some big competitions stock. I swore I'd never get another FX....but I did. Got the .25 compact tactical with bottle in .25. For pesting the ease of changing power levels and the adjustable AR type stock is more useful than is obvious. Nice magazines, Good shot count especially on low power. I shoot mostly all my shots on low power. At 25yds I can bag any bird on the feed pile. Use JSB Hades on all the rifles and they shoot just fine in any of them. 

So...Check the Lelya 2.0 and the FX tactical combat which is a Dreamline with countless options to make it what you want it to be. I have all the above because I like to shoot. I don't like to fuss with the innards, but have high respect for those who do and do so successfully.


 
If OP doesn’t intend to shoot slugs or shoot light slugs the .25 wildcat will be most versatile and capability of taking games up to small predators. As much as I’m obsessed with .177 guns it’s a niche caliber for small stuff, if I had bigger stuff to shoot then the 700mm .25 barrel will go right back onto the impact with heavy slugs loaded. 
 
I was in the same boat, I have a AA S510 in 22 and it was doing the job for jackrabbits (not many squirrels here in southwest Utah). My prob is the stocks on the gun are too nice for a hunting gun. I like the shot count of around 90, but I need a bush gun. So after a ton of research and advice, I ordered the AGT Uragan in 22, it gives me 200 shot count, and thats all I need for an entire day of shooting without having to refill. I considered the 25, but 22 is doing everything I need right now, so.

I'm also considering getting a big bore for the bigger game once the S510 sales, and then I will be covered if the 22 wont get the job done. Good luck