I've made several baby quilts. I always like Warm and Natural. The more you wash it, the softer and better draping it will be.
No -no to invisible thread, and make your stitches very close so that tiny --or toenails!!-- can't get caught in them. I don't typically quilt densely because I like them fluffy. So about 1.5-2 " is my general guideline, not my rule.
i stay away from fleece since it doesn't breathe. I love flannel for a city, warm batting, and there are some adorable flannels out there. I like what Thousands of Bolts offers.