Economical Low powered gun suggestions

Did you look at what Krale may have to offer? Sometimes the price + shipping is even less than buying local and a lot of their guns are available in different power levels. 

https://www.krale.shop/en/sport-shooting/guns/air-rifles.html?energie_filter=577&powersource=3374

It might go a little over $500 but you can turn down the power to around 12 fpe in a Kral PCP .

You could use a .177 Hatsan AT44 and change the valve to a non PAL valve for $20 from Canadian airgun forum. That would put you at the 12LBS and under $300. If you pick up a Amazon hot deal at $272 with your valve of $20, your under $300.

I bought a HW 30 and cut a loop out of the spring. I tried a Benjamin 392 but I could not get any accuracy out of it. AOA has a sale on HW 30. $250 which is a good price for what you get.

1720t with carbine stock. Throw in a huma reg and 40 shots at 12 fpe. Accurate, light, hand pump friendly. Just plain fun to shoot.

Maybe a used Air Arms T200 from the Civilian Marksmanship Program? ($525) They have other offerings as well. I bought two Avanti 853's from them and they have been great plinkers.

You could get a PRod set up with a hand pump and maybe squeeze in a chronograph for $500. You can tune it down. Also the Benjamin G2 Fortitude is about to release, at the shot show Phil from crosman says it's adjustable from 10/12fpe to 20/21fpe. These two options can be set up for lefty use if your one of those

I also recommend the Air Arms T200. The trigger is fantastic out of the box and it's accurate. It's the most accurate shooting off-hand for me due to the light weight and great trigger.

How about the S200 from Air Arms? I think it is rated at 800 fps (7.0 grain pellet?) Which would give you about 10fpe. There is also the S200 Hunter that uses a 10 round magazine. These are a little bit over your $500 limit but I'm sure you could catch a sale on them.

I went and checked the S200 at PA. 800fps with 7.9g pellets (12fpe). The Hunter version is .22 cal. $599 for either model.

I have a CZ200S in the red laminate stock that is pretty much like new (shot around 200 pellets) I will sell it for $500. I have the box and accessories. Comes with the CZ scope and mounts still unopened. I bought 2 of these. One for my wife and one for my daughter. I set my daughters up and she uses it some but my wife never really showed interest. Therefore I am going to sell her's. Just PM me if you are interested. I planned to get the box and all the stuff together this weekend and put it on the classifieds next week. Since you are looking for a 12fpe or less PCP for $500 I figured I should say something. Like all CZs it's super accurate. It's this rifle: https://cz-usa.com/product/cz-200-s-w-scope/ It was discontinued in 2011 but I got one new from them 2 years ago. I happened to meet the president of CZUSA at a sporting clays shoot and she told me she had a few that had come in so I bought a couple.