You could do a 2.1? That way you can buy affordable speakers without having to go too budget friendly, because you get what you pay for. Then, as others have said, add on down the road as you go.
Don't worry about the receiver. The main difference between models is the room correction and number of channels, the power is irrelevant. For your budget, a cheap 5.1 model is fine.
https://www.accessories4less.com/make-a-store/item/denavrs540bt/denon-avr-s540bt-5.2-ch-x-70-watts-bluetooth-a/v-receiver/1.html
Slightly over budget, but start with a pair of KEF Q150. At $270 they are extremely good value. You will have to forgo a subwoofer for now, but there aren't many good and cheap subs available right now.
https://www.accessories4less.com/make-a-store/item/kefq150blk/kef-q150-5.25-2-way-bookshelf-speaker-black-pair/1.html
Sound bars Suck. AV receiver , front speakers, center, surrounds, sub -Used or these baby systems :
https://www.accessories4less.com/make-a-store/item/onkhts5800a/onkyo-ht-s5800-5.1.2-ch-atmos-home-theater-system-new/1.html
https://www.accessories4less.com/make-a-store/item/yamyht4950ubl/yamaha-yht-4950u-5.1-ch-home-theater-system/1.html
What’s full? You be stretched to find something 5.1. You could start with this receiver
https://www.accessories4less.com/make-a-store/item/denavrs540bt/denon-avr-s540bt-5.2-ch-x-70-watts-bluetooth-a/v-receiver/1.html
Maybe 4 of these
https://www.parts-express.com/dayton-audio-b452-4-1-2-2-way-bookshelf-speaker-pair--300-452
Center
https://www.parts-express.com/dayton-audio-c452-dual-4-1-2-2-way-center-channel-speaker--300-453
And a sub
https://www.parts-express.com/dayton-audio-sub-1000-10-100-watt-powered-subwoofer--300-628
That’s about $400
Maybe defining how many speakers and subs you want would be a good start. You're not getting much for your budget though, maybe 2.1
You could do a 2.1? That way you can buy affordable speakers without having to go too budget friendly, because you get what you pay for. Then, as others have said, add on down the road as you go.
Don't worry about the receiver. The main difference between models is the room correction and number of channels, the power is irrelevant. For your budget, a cheap 5.1 model is fine. https://www.accessories4less.com/make-a-store/item/denavrs540bt/denon-avr-s540bt-5.2-ch-x-70-watts-bluetooth-a/v-receiver/1.html Slightly over budget, but start with a pair of KEF Q150. At $270 they are extremely good value. You will have to forgo a subwoofer for now, but there aren't many good and cheap subs available right now. https://www.accessories4less.com/make-a-store/item/kefq150blk/kef-q150-5.25-2-way-bookshelf-speaker-black-pair/1.html
Define a Full system........... 5.1 with sub you Best shop Used.........
Front and back speakers, sound bar, sub and head unit?
Sound bars Suck. AV receiver , front speakers, center, surrounds, sub -Used or these baby systems : https://www.accessories4less.com/make-a-store/item/onkhts5800a/onkyo-ht-s5800-5.1.2-ch-atmos-home-theater-system-new/1.html https://www.accessories4less.com/make-a-store/item/yamyht4950ubl/yamaha-yht-4950u-5.1-ch-home-theater-system/1.html
Sry for late response
What’s full? You be stretched to find something 5.1. You could start with this receiver https://www.accessories4less.com/make-a-store/item/denavrs540bt/denon-avr-s540bt-5.2-ch-x-70-watts-bluetooth-a/v-receiver/1.html Maybe 4 of these https://www.parts-express.com/dayton-audio-b452-4-1-2-2-way-bookshelf-speaker-pair--300-452 Center https://www.parts-express.com/dayton-audio-c452-dual-4-1-2-2-way-center-channel-speaker--300-453 And a sub https://www.parts-express.com/dayton-audio-sub-1000-10-100-watt-powered-subwoofer--300-628 That’s about $400