Wow,
@Scotay42 covered literally everything I was going to type lol.
BC has their upgraded Maverick 30Cal on sale again. I would call them and see if they would take a little more off the top. But even at their listed sale price still a decent deal for a new FX imo. Even comes with some ammos.
Elevate your precision shooting game with the BC Custom Maverick Shooters Package in .30 caliber, featuring a 700mm barrel length. This comprehensive air rifle package blends cutting-edge technology, adjustable features, and expert craftsmanship to set a new standard in precision shooting...
bulletcentral.com
And for a starter compressor the GX CS3 is a good option, and is currently rebuildable which is nice. They have coupons on amazon from time to time and you can find them for just over $300 sometimes. I would also keep my eye out for a used AGT Uragan or Vulcan, FX Maverick Wildcat Impact DRS Panthera etc here in the classifieds.
ETA: To complete your package a UTG Accu-Sync mount is a sturdy budget scope mount, and pick a decent 30Cal Moderator and that should keep you right at your total budget goal. Also I wouldnt dismiss a 25Cal, a stout pcp will be able to ethically take down a coyote. My Impact MK2 does an easy 80fpe and I would use it on a coyote if I had to, and I admittedly am on the more reserved side of the hunting ethics conversation.