If you're meaning $300-400 total then a springer may be more in the budget because like JDR is saying you need a good scope which will cut into the budget. Just make sure it is rated for the double recoil of a springer! UTG works.
I've used my Crosman Fire since 2015 or 16 and Crosman Diamondback for a couple years with success. Benjamin/Crosman gas ram tech is good stuff especially the Elite. I always forget how quiet my Diamondback is. Although that thing is heavy..it is pretty powerful. 18 FPE. And has "iron" sights so a scope isn't necessary.
They make break barrels that have rotary magazines built in now but with my friends dad's experience with the Gamo jamming frequently and some ratings I've seen on Crosmans I would just go the single shot route and get a
pellet pen . Manufacturers make the gun cost a certain amount and the way I see it them putting $ into the magazine mechanism takes away from $ going into the gun fit and finish etc.
Personally I wouldn't pay that much ($3-400) for a break barrel cause my $100 do about the same I mean Mr Squirrel doesn't care if your gun has a turkish walnut stock etc LOL But you do get more accuracy to a point.
But if your budget is $3-400 for just the gun then check out some PCPs. For a carbine, everyone seems to love the Notos which would easily be in that range. You'd need a fill source but I think you'd do best with a hand pump for $60 from
Amazon. For a rifle I'd recommend the Avenger for sure, I love mine. You'd do well to add a
LDC though. Pumping is possible just more pumps to fill.
The other recommendations are good too I just don't believe in un regulated PCPs. I get you can have some more power and could achieve good consistency in FPS in a certain range of shots but it's 2023 and I think the tech is there with the ultimate air gun being a regulated pcp.
Beerthief is right though a springer is just grab and go, it won't ever run out of air! So basically this depends on your total budget for what to get cause you'd need a scope for either but add a pump for PCP.
Whatever you decide let us know what you end up with!!!