My strategy is to work the places that can easily be worked first, always making sure that where pieces meet, the fabric will lie down properly. Pretty much means working edges inward. It helps to have two needles going, sometimes.
I am doing a combination of folded-under applique and raw-edged. Probably, with the possible exception of that red velvet, this quilt will be entirely hand-quilted.
You may remember this bleached red plaid from the Happy Hut Quilt that I made for D. (that red plaid flannel was used, one December not long ago, to make his pj bottoms – a traditional Christmas Eve gift in this house (though I will admit to buying the pants in the last couple of years)).