Well, Neo Geo home cartridge shooters + cheap price = not many chances. Basically Alpha Mission 2, Ghost Pilots and Last Bade.
Ghost Pilots: Well, it is very challenging, and you can have fun with it, but it is nothing special. It’s an old game. It practically has no replay value. You can buy better plane shooters in for other systems.
Alpha Mission 2: Well, perhaps better than GP, but again is an old game.
Last Blade: Challenging game, it evokes R-Type quite a lot, great atmosphere, it looks great even though it is an old release.
Forget about Pulstar and Blazing Star Home carts, they are going to cost you one of your legs and part of the other.
The Sonic Wing series are good to, but you will be very lucky if you find a Sonic Wings 2 in Mint Shape for less than 130 USD. These two are cheap in CD.
If you are looking for a commando type shooter then your best chance (because of price) should be Metal Slug 3 or 4, in this order, but be prepared to spend at least 250 USD.