A number of years ago I did a lot with computer printing on fabric. It can work very well, you actually don't even need any special fabric, you can just press your fabric to freezer paper or do other things. The prepared fabric sheets are often in the specialty area of paper at your local office store!
A lot (a huge lot) depends on your type of print Laser, Ink, Jet, etc. Follow the recommendations for your brand of printer.
I haven't used them yet myself, but it might be worth some time on Spoonflower to design/print it there.
https://www.spoonflower.com/
Several board members have reported highly about their experiences with the site and then the delivered fabric.