Since you are going to design and make this you have to select any of the hundred plus Bluetooth audio receivers than that goes to the any thousand models of amplifiers to drive these speakers.

Frankly I decided to forget all that and picked up a nice enough set of Bluetooth enabled amplifier and speaker book shelf speakers to get away from making a solution.

There's nothing wrong with making your own today. But to select one solution is going to be your choice here.

A tip though. Be sure to use Amazon best sellers to cut through the hundreds of models.

Example: https://smile.amazon.com/AmazonBasics-Bluetooth-4-0-Audio-Receiver/dp/B00I59VBH4/ is all of 20 bucks. Done?

More at https://smile.amazon.com/Best-Sellers-Electronics-Wireless-Audio-Receivers-Adapters/zgbs/electronics/10110414011/ref=zg_bs_nav_e_3_322215011