Sounds like a Gamo Urban would be a good fit for you. I have one and love it. It's extremely accurate, lightweight, and very hand pump friendly. The bolt is also ambidextrous. Walmart has them now for $259.
I have a gen 1 storm rider. I actually had to chamfer the breech end of my barrel to get the pellets to load correctly. Up until then I had just used the single shot tray and still had a hard time. Now that I did that it shoots with the mags and cycles perfectly with redesigned monsters 25.39 gr JSB's. I get 20 good shots coming in at 30 to 35 fpe and accuracy is pretty good too. If your worried about the barrel flexing they do sell barrel bands at PA for ten bucks. This gun is very pump friendly. I don't own one but the benjamin discovery may be an option to keep in mind too, it's only a single shot but I do believe there are some manufacturers that make multi-shot breeches for it. The gamo urban would probably be a good choice too however I do not own one. There are some refurbished options out there as well just have to keep looking until you find what your looking for. I just got a marauder from field supply back in December for $325 which is an awesome deal. If your budget will allow for just a little more you will get a better gun, at least that's what I have found out so far. Oh yeah another option is that crosman is going to relaunch the fortitude this spring. That would be a little more than 400 for the pump and gun but it may be worth it in the long run. There is a lot of choices out there that's for sure. Have a good time shopping around and keep in mind that once you get the rifle I almost guarantee you'll want to modify it lol.
A Crosman Discovery / Maximus is a 2000psi charge and very hand pump friendly.There are several aftermarket breeches to make it left handed, some are ambidextrous and can be oriented ether way. Check AlchemyAirwerks, Magnum airpower, and Alliancehobby... they all have a version for "southpaws" even if you aren't. It is an easy swap at home and there are tons of other tid-bits available for future mods.
This is one place where a Benjamin Marauder still runs up front. If you watch for deals you can buy one new nowadays for $350 or less. The bolt is user switchable to a true left hand in just a few minutes time. They are quiet and have good triggers out of the box. They don't have the best shot count when new, but it is servicable, and $60 and a little work (requiring a chrony) will fix that issue too. As for the Urban, I have a BSA Scorpion SE which has a nearly identical action. I switched the bolt to the left side for "quasi-left" action. The bolt has a very short throw and holds in place quite well, and I have found that i rather like it. Yeah, I'm all lefty.
And there is the Pump action AT-44https://www.pyramydair.com/product/hatsan-at44-qes-pcp-air-rifle-open-sights?m=2779 May find a refurb cheaper at Hatsan USA or the like.