You seem to want to go with a Sony Receiver. I have a Sony STR-DN1050 and two Denon setups (and had 2 older Sony's in my past life. All have been good.) so I know these OEMs a fair bit.
If you are headed to Sony, and want Bluetooth and WiFi you need to move up at least one level from the above STDH550 towards a STR-DH770 for Bluetooth, and into at least a STR-DN850 for both Bluetooth and WiFi.
Sony's recent model history has them change a digit in the model number each year. There are some changes each year. For example the STR-DN1030 became the STR-DN1040, then STR-DN1050, then STR-DN1060, then STR-DN1070, and now the STR-DN1080.
Seeing as you went for some deals on your Speakers buying them used, you could save a bundle doing the same with a receiver. (I bought both my Denon receivers used.) For a used Sony look for the STR-DN1050 as it should suit your needs and be less than half retail by now.
Or, we don't know what country you are from so please advise, there is a good deal on a Denon AVR-S720W at Accesories4less for $290 with a 2 year warranty but => Sold exclusively within the US only. No shipments allowed outside the US!