Haven't done any quilting for years, but the stuff which is about an inch thick(when puffed up) should be ok. You might need to experiment with needles though. Your handbook may suggest the best size. I'm sure a keen quilter will be along soon!
Do you mean fit in the throat of your machine? i.e. the gap between the needle and the upright where the stitch dials are?
When I do buy quilt wadding (I sometimes use old blankets too) I buy a cotton bamboo blend and I can quilt a decent sized single on my machine (a mid-range Husqvarna Viking) without too much trouble. I could probably manage a small double if I had to, but I think much more than that would be a real struggle. It's pretty much the thinnest wadding I've come across, but someone may be able to advise differently.
When machine quilting, you need to put the feed dogs down so you can glide smoothly across the fabric. Also, what helps a lot is using a "walking" foot on your machine. This type of foot is ideal for quilting as it helps feed the layers of fabric smoothly through the machine with no snags, or wrinkles. If you are going to be regularly quilting, I'd say it's a must-have.
I stopped using manmade wadding and use only natural fibres which are much warmer. I also find it easier to sew as the polyester feels sticky and catches on the needle. You will need to roll the quilt up under the sewing arm of your machine when you do the quilting. Try Cotton Patch for a good range of waddings. Old woolen blankets are also a good source of wadding.