For a super simple setup I would use the Karafun app on the ipad.

A wired connection from the Ipad to a speaker will sync the words and music better than a bluetooth connection. But you might want to try bluetooth and see if it's an issue for you or not, I know the delay annoys me.

Since you said it doesn't have to be super loud you might want to consider just buying karaoke microphones like these.

https://smile.amazon.com/M100-Microphone-Bluetooth-Wireless-Portable/dp/B08NSYDWDM

And then play the music through any speakers, including your home AV speakers if that's an option.

I general wired mics are a simpler option than wireless.

There are many posts on here that give valuable information about speakers and mics including links to specific gear. I suggest you read some to help you narrow your search.