After doing a lot of research, I purchased a Sizzix Big Shot Plus. I absolutely love it. It easily and accurately cuts through 8 layers of cotton fabric. Sizzix offers a variety of dies, but the ones I use the most are the 4-1/2" strip; 2-1/2" strip; 4-1/2" square; 4-1/2" two piece triangle; and 4-1/2" four piece triangle; and 1-1/2" strip. There are dies for appliques too, but I don't usually do that. I chose the Sizzix over the Accuquilt because:
1. the Sizzix system and dies are cheaper (i.e. the 1-1/2" strip dies on Amazon - Accuquilt = $102.50; Sizzix = $44.88)
2. the Sizzix cutter can use Accuquilt Go dies, but the Accuquilt is limited to only their dies.