If you want to do a lot of plinking, the Hammerli 850 is a lot of fun but you need to spend more serious money on getting plenty of mags, more OEM factory O rings, plenty of lubricant to lubricate the magazine rubber gaskets, a lot of CO2 because it's cheaper per charge in bulk as well as the proper pellets, maybe a scope. To properly outfit one you might need to spend 1.5x to 2x your budget as it starts in the 300's.
50 yards is a fairly long stretch for any non PCP air rifle. If you want to keep things inexpensive I recently picked up a Benjamin GP 22 cal on the cheap. It is one of the lower cost break barrels but the gas piston is lower maintenance, does not need relubrication, is a lot quieter and can stay cocked for longer so it adapts better to hunting and pest control if you eventually decide (or need) to shoot some flesh, feathers or fur with it.
I really like this rifle and have others like it but more powerful because I found several of them online at steep discounts and made a lowball cash offer at a local gun shop that wanted to get rid of it. I think with a lot of practice and a better scope with the higher power versions that shoot flatter you might get just beyond 50 yards but until the gun breaks in and you get good at shooting this type of gun which behaves differently with its recoil divide that distance in half or even shorter range.
I just posted somewhere else that after doing my part which I will describe below using Crosman type pellets I can
-stack pellets at 10 yards
-shoot keys off a keyboard at 20 yards
-hit shotgun shells at 30 yards consistently.
-consistently hit cans at 30-40 yards.
-consistently hit a steel target or 2L soda bottle at 50+ yards but both are typically bigger targets than usual, certainly of a size that would not allow proper shot placement on an animal with such a large kill zone with its reduced energy at that range and not be humane. I must stress that I do this for challenge and even using larger targets the accuracy, while decent, drops off noticeably after 40-50 yards for most things for which you want to use this rifle.
Based on this observation I would say the absolute vertical limit for this is 50 yards but you have to do your part indeed. I have not found higher power rifles to be any more accurate or have much better range relative to the cost (another 5-10 yards vs 50-100% more cost). To the opposite more powerful rifles are heavier, have more recoil and tend to be a bit less accurate and difficult to shoot as well as lending quickly to fatigue that spoils your aim due to high repeated cocking effort. There is a certain fun element of hurling a 25 cal, 25 grain lead pellet at 750ish FPS at household items otherwise slated for trash you wish to "modify" pre landfill trip but that's beyond your scope, no pun intended.
Break barrels have reports of accuracy all over the place. In my experience half of it is break in and cleaning, the other half is technique; they do not shoot like a 22 and some of the more powerful ones will have recoil somewhere in between a 22LR (basically almost none) and a high power 30 cal rifle that is strange and needs management that is different from real cartridge rifles.
Don't take nor require the accuracy seriously nor try too hard to sight in the scope for the first whole tin of pellets, just use it to get familiar with the rifle and develop good technique. After about 200-500 pellets clean the barrel, then shoot another dozen or two "fouling pellets". At that point you can start seriously sighting the scope in to stack pellets and reproducing the above results if you have gotten a feel for recoil management and how a break barrel rifle should be held, namely with an artillery hold and any such other way to mitigate the bidirectional, front/rear recoil that occurs. You can try benchrested but best accuracy for me is just to lie it on top of my forearm which in turn is flat on some other surface like a fence, deck rail or what not.
While your mileage may vary, I just mention the Benjamin GP because it's the least expensive, works well for what it is and though has a very, very long trigger, more or less behaves like most offerings of this type of gun but the piston vs spring design allows quieter operation. Most of these guns are not as different as you think, the above rules apply for nearly all of them, though the more expensive ones are more refined with better triggers, the more powerful ones tend to require much greater cocking effort and be quite ungainly to carry as well as have a shorter expected lifespan so don't be excited to get a "magnum" especially if hunting larger varmints is not your thing.
Don't forget to buy 2-5 shatter resistant eye protective devices of your liking. You will need a number equal to as many people as you anticipate shooting with you at the maximum (wife, kids, siblings, friends) plus 1-2 extra because they break, get scratched, or get lost and you never know how many people might be around shooting with you. They are super cheap and to a shooting veteran, absolute common sense to wear 100% of the time like seat belts in 4 wheel vehicles or helmets in 2 wheel vehicles.
