Dear Jade,
If you want to sew your bindings on the machine by all means do it, because you are right, this is supposed to be fun!
To make it easier remember to trim your quilt edges to be straight before you begin to bind it. The rough edges of an untrimmed quilt may not look like trouble, but the dips and itty bitty uneven edges, can keep the binding from laying flat while you are sewing it.
Some machines come with a curly little binding foot that is ever so easy to use. You just thread the binding through it and sew! It sews the front and back at the same time!
When you get around to the starting end, you just cut the binding to overlap about a half inch, fold it under and stitch a bit past the joint.
The nice part of using this foot is that you just sew around the quilt once!
But! wait....practice first! make some potholders or mug rugs....or even some placemats!