I think one is going to have to get a separate AVR and blu ray disc player, but with the modern HDMI cable(which transfers all video and sound) there is no need for lots of cables. One cable goes from disc player to AVR and that's it. It doesn't matter if you want 3, 5, or 7 channels of sound.
Hoping that the OP is also not wanting speakers for the budget mentioned, but I'd suggest a mid range Denon AVR and an Oppo 103, the whole thing should not run over $1500. You can get refurb Denons and Marantz AVRs at Accessories4less.com(no affiliation) or brand new in box if you phone them to check for availability.
And don't spend a lot on the HDMI cables. You may only need one if your display doesn't have an HDMI jack.
Hoping that the OP is also not wanting speakers for the budget mentioned, but I'd suggest a mid range Denon AVR and an Oppo 103, the whole thing should not run over $1500. You can get refurb Denons and Marantz AVRs at Accessories4less.com(no affiliation) or brand new in box if you phone them to check for availability.
And don't spend a lot on the HDMI cables. You may only need one if your display doesn't have an HDMI jack.