AN ALL-ROUND GUN? I have always been looking to buy
all-round guns...! And like you, I started with a powerful springer, and realized what I'm looking for could only be found on The Dark Side (the PCPs).
I won't recommend a certain gun — there are too many features to consider — and gun beauty is in the eye of the beholder, so you need to surf the web yourself....
Some comments on your requirements: (1) Quite enough for backyard shooting: Any PCP .25 and under can be made backyard quiet with a silencer ($100-$200). I have a Silencer Specs Table to compare over 50 models, if you're interested.
(2) Reliable and easy to work on (when/if needed): For
reliable you might want to stay away from Chinese products. Though, they can be easy to work on. YouTube and the forums are your friend.
Having a set of o-rings for your gun on hand is always a good idea — they are bound to need replacing eventually.
Some brands that are said to be extra tough: Taipan, AGT, Ataman, and especially EDgun (the owner drove his truck over one and then shot a target at 50y).
(3) Something I can hunt with some (probably in .25?) (from Crows up to perhaps a raccoon at closer range): Raccoon are pretty big and tough, but at "closer range" of say 15yards, they can be taken with smaller calibers. You want to do the same at 40 yards, well, then .25 sounds better (at least with the gun's power as set by the factory), or use a slug which delivers much more power at longer ranges, or dial the power up....
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Caliber: The power potential of recent PCP's has risen steeply, so that you can deliver a lot of power even with smaller calibers, like .22cal.
Some guns can be adjusted externally (mainy of the FX models; adjustment of the regulator allows a wider range of power adjustments, the hammer spring tensioner is often accessible from the outside but only allows adjustments within a limited power range). All guns can be adjusted — just watch some YouTube videos and ask on the forums.
The .22cal seems to be a good all-round caliber, with way more pellets and slugs available than in .25cal — but delivering much more power than .177cal, and easier to handle bec. they not so tiny.
(4) Target shooting comfortably behind a bipod (up to and beyond 80 yards to stretch it out): Any gun can be mounted on a bipod and aimed at a target.....
(well, the EDgun Lelya 2.0 and the Ataman BP-17 maybe not).
So, are you hoping to compete? Then you'll probably want a dedicated gun for that duty.... Otherwise, most PCP's will get you 2" groups at 80y, many will get you 1", and some even less than that (provided the shooter does their part, of course
).
(5) Not too heavy (see hunting): Well, in comparison to springers PCPs are much much lighter. And going with a synthetic stock and a bullpup format even lighter.
(6) Doesn’t have to be babied when carrying around (see hunting again): Cf. point (2), "reliable."
Some guns have "freefloating barrels" — I take that to mean that the barrel is only attached on one point — the action. The rest is free — and therefore when getting bumped or when leaned against a tree the gun could loose zero, or at least the point of impact could shift for a time until the barrel returns to its original position.
Of course, the longer the barrel is the larger the negative effect of such a bump or leaning.
For that reason, I
personally will not buy (for example) an FX Dreamline bullpup, but I would buy the FX Wildcat (where the barrel is also attached to the scope mounting).
(7) Doesn’t cost much over $1500 (hopefully less): That's easy to do. How nice you have that kind of money available.
Have you considered the following features?
(8 ) Large magazine capacity (20 and more shots; FX offers that) vs. normal capacity (around 10)?
(9) Bullpup vs. traditional rifle?
(10) Action — with a lever vs. with a bolt?
(11) Lever position on a bullpup: close to the trigger, or close to the action?
(12) Air bottle (large capacity of shots) vs. air tube?
(13) Maximum fill pressure? 300bar is pretty high (hard on your compressor, or if using a CF airtank, you won't be able to fill it up all the way after a while as the pressure in the airtank will go down). 250bar or less is more manageable (I have handpumped up to that pressure for a couple of years). But 300bar allows more shots from a comparably small airtube.
(14) For an all-round gun it could be interesting to be able to swap calibers, swap barrels (longer barrels for more power; or slug barrels more suitable for heavy slugs, for example). FX is the brand that usually offers this advantage.
Have fun gun shopping!
Matthias