Not sure you have to spend all your budget but that is a good place to be. There are several good streamers in the $5k and under price range. Biggest difference is abilty to do roon and controls. to me the big 3 are arurender, innuos and auralic. Aurender sees roon as a competitor and doesn't support roon so stay away from aurender if you want to ever use roon. If you don't use roon, then the control software on each system will be important to you. I chose Innuos. It does roon and controls from a phone ap.
after the streamer you should probably upgrade the digital system feeding it. make sure you have good quality ethernet cable from your router. For digital, i like cables with silver coated copper. Not necessarily terribly expensive. Audioquest has several levels that work for me. install an upgraded 'audiophile' switch. I used etherregen. the switch plus calbles will run you a grand or a bit more.
Jerry