For sewing the binding I use whatever needle is handy at the time. Granted, that's usually a between as I hand quilt, but sometimes not. Sometimes I use hand quilting thread, sometimes just general sewing thread...whatever is the correct color for what I'm sewing.
As to mending (sewing buttons, etc.) I hate that! But for all purpose hand sewing, I use any general hand sewing needle that is close to the correct size for the job. Now that really didn't help much, did it? Sorry.