Hi Bunny
I just wanted to welcome you to the board, and make a suggestion to try while you're deciding which machine to choose.
Have you tried increasing the pressure to your presser foot? My machines all have a screw or other mechanism on the top that allows you to adjust -up or down- the amount of pressure the foot applies to the fabric. Maybe your machine is set for a lighter weight fabric by default. Just a thought. Also, slowing down is very good advice.
good luck