I would like to play MP3 files from iTunes and also Spotify as well.
I guess you're looking at Apple's Airplay protocol, or the more open DLNA.
iTunes will support the former, but, I don't think it supports DLNA. There are, however, plenty of apps that will play music stored on your iPhone to a DLNA device.
Spotify should also support DNLA.
Then you can pick any one of a number of DLNA renderer devices, of which there are loads to choose from. One cheap possibility is a cheap, secondhand Android phone, with the phone bit disabled, running one of a number of DLNA renderer apps (of which there are many more to choose from than on iOS), streaming via WiFi. I use BubbleUPnP, which is a complete media player sustem (DNLA server, controller & renderer).
I also have a little box called a SoundMate M1, which is a DLNA renderer (it also claims to support Airplay, but I've never tried that). I think it's now unavailable, but there are plenty of similar no-name devices. Mine was £18 delivered a few years ago. 3.5mm audio of optical SPDIF output.
https://www.amazon.co.uk/SoundMate-Wireless-Streaming-Receiver-Airplay/dp/B0195AEBBO
This looks and sounds (reads) pretty similar:
https://www.amazon.co.uk/Neet®-Wireless-Receiver-wireless-streaming/dp/B00O0U37HO
Then there's Chromecast Audio...
The best sound...? Low budget? Always going to be a compromise. Also depends on your view of 'low budget'; mine would be £30, but if you're considering a Connect (which I think is massively overpriced), maybe your budget is higher than mine.