Recommendation - Don't use a bigger needle. It will just make bigger holes in the quilt sandwich.
I've been using my Featherweight quite successfully in FMQ, with all types of thread - Coats & Clarke, Aurefil, Hand quilting thread - both polyester cotton coated and 100% cotton are the most I've used so far. Older thread will break, especially older 100% cotton thread.
I get skipped stitches if I move the material too quickly for the speed I am sewing, or I have a dull needle, or my needle is not properly threaded or the needle is installed incorrectly in the machine (i.e. backwards to where it should be).
The thicker the thread, the larger the needle you have to use to help cut down on thread breakage. Coats & Clarke is thicker than Aurefil because it is predominately used for clothing and general sewing. I generally use a 14 needle for Coats & Clarke (generally 30 weight), and an 11 needle for 50 weight Aurefil (which is a lot skinnier than Coats & Clarke).
Both produce beautiful FMQ with practice. It just depends on what you have available to use and how much practice you put in.
I would say I am an intermediate FMQ'er - past the beginner stage, but not good enough to just sit and do it.
PRACTICE, and work with the needle/thread combo until you have something that works. There were days when I would SWEAR everything was done correctly, and yet I would still have problems. Some days I just want to SCREAM because the stuff just doesn't want to flow. Then you will have days when the moment you sit down it flows beautifully. So DON'T GIVE UP. Just do it as the advertisers say! You can do it and you will be very happy you did!