Hi Jim
These days most people do multitrack using a DAE (Digital Audio Editor), sometimes called a DAW (Digital Audio Workstation). These run on computers of most persuasions. You can have as many tracks as your computer's resources will allow (and that's usually lots!). The cheapest is Audacity (free!) but it does lack some desirable features for multitrack work. You might like to look at Reaper. It's only $60 for domestic users, and they offer you a 60-day free trial to help suck you in.
Suggest don't start your free trial until you have everything else ready to go. Everything else will include:
- a microphone and whatever you need to connect it to the computer (a USB condenser mic is nice and they are really cheap these days!)
- a suitable stand for your mic (the back of a kitchen chair and some duct tape if you have blown all your money on flutes!)
- some (preferably enclosed) headphones, to listen to playback while adding the additional tracks
- decent speakers are nice for mixing down. You could snitch them from the HiFi ....
- a couple of sets worked out in principle and practiced as much as you can without the technology....
https://www.reaper.fm/I'm sure there are many of us who can help with any issues you encounter.