cricut vs accuquilt
 

I am interested in purchasing a machine to cut quilting squares, but also maybe vinyl. Any suggestions or advice?

Welcome to the board. I have not heard of anyone cutting vinyl with ones.

cricut can cut both, bit a silhoette and scanncut do better IMHO. I haven't heard of an accuquilt cutting vinyl

Accucut can cut vinyl. I use it to cut wood veneer for inlay marquetry and have cut chipboard with no problem. With the accucut products, you have to purchase dies that are dedicated to a specific size & shape. If you cut lots of strips, squares, triangles etc. that's a good choice. You can cut multiple layers without a problem. If you do a lot of applique and are only going to do a small number of a specific design, then a computer operated cutter might be something better suited.

I wouldn't buy a cricut. There are too many limitations. For one, you have to be online to cut. I don't think they can cut thicker vinyl (the type you'd sew with) but I've never tried.