Yeah forget 240v then completely for $500. That's not going to happen since it has to be wired into your panel. You'll need to do extension cords.

Your pellet grill is 120v.

Take that 240 stuff out, and you're golden:

https://www.homedepot.com/p/Champion-Power-Equipment-4500-Watt-Recoil-Start-Gasoline-and-Propane-Powered-Dual-Fuel-Open-Frame-Inverter-Generator-with-CO-Shield-200978/320192063

https://www.walmart.com/ip/Champion-Power-Equipment-4250-Watt-Dual-Fuel-Pull-Cord-Start-Inverter-Generator/768057179?wmlspartner=wlpa&selectedSellerId=101017883

This may be closest to your $500, with some decent power:

https://www.walmart.com/ip/Sportsman-3-500-Watt-Dual-Fuel-Inverter-Generator-for-Sensitive-Electronics/383227775?wmlspartner=wlpa&selectedSellerId=0

If you want a REAL gas sipper:

https://www.homedepot.com/p/Champion-Power-Equipment-2500-Watt-Recoil-Start-Ultra-Light-Portable-Gas-and-Propane-Powered-Dual-Fuel-Inverter-Generator-with-CO-Shield-201122/318783386

https://www.amazon.com/Pulsar-Generator-Capability-Compliant-PG2200BiS/dp/B07J5HD8L9?source=ps-sl-shoppingads-lpcontext&ref_=fplfs&psc=1&smid=A2LH8DUZ1Q6T63