Sky is important to me. If there is detail up there (heavy overcast or bright blue sky without clouds don't have much detail), I want to pull it out. Depending upon where the camera metered when you took the shot, the sky will be bland. Try pointing your camera at the sky (just above the horizon) to let it meter there. The end result will be a nice looking sky, but what's on the ground may be underexposed, but you can brighten that in post.

In LR, I crank highlights way down to get detail in my sky (some contrast will help here too), then use shadows to bring brightness to what's on the ground. I always use -0.3 exposure compensation. I set it there and leave it, for it's easier to brighten a area in post than it is to get detail from blown-out brights.

I took these shots at sunrise the other morning. I hope they are indicative of what you are trying to achieve.

The 'Before' shot shows the buildings on the ground as brighter, because that's where the camera metered, and it allowed more exposure. After bringing the sky to where I wanted it, the buildings on the ground looked darker, but it's more realistic as it was sunrise and all the light had not yet reached all those shadowed areas. Much more realistic scene.

Definitely lives with a quilter. Everything here is correct. Quilting is a study in geometry and skillful color choices, blended with repetitive patterns as much as it is art. If you ask you quilters before you shoot, you will probably find they want to show the whole quilt. So much work goes into every inch, they want people to appreciate the whole thing.

Soft uniform light, hang them as even as possible, and use your tripod. Don't spend time overthinking this out. If you had a chance to look at the quilts in the book I mentioned, a couple of those images were sent to me from relatives overseas. They just had simple cameras, but good post processing made them work out just fine.

There is good information above, though I am not in complete agreement with all of it. First, my experience with quilters (I share my bed with one) is that they want it shown in its full glory, the whole thing flat and all at once. That means hanging it. (Laying it on the floor of that garage would make it very hard to photograph straight on, and just suggesting that you might lay them on a garage floor could get you seriously hurt.

You want your camera on a tripod set exactly at the quilt mid height, centered with no offset or skew! This will minimize the post processing adjustments to make it appear square. Lighting is crucial - it must be even over the entire quilt; if you can find an outdoor north facing wall on a windless day, that might be your best bet. (I used that method to photograph some artwork for a client. The other way was in the studio with four strobes with shoot through umbrellas or soft boxes set at 45 degrees from the quilt surface - we used cross polarization for critical artwork. Of course that was back in the film days, so now you could use other light sources if you corrected white balance carefully, and made sure to have even soft lighting over the entire quilt surface.)

You will need the means of hanging the quilts (a quilting club might have that covered, otherwise a background system would work), a good ladder system to get to everything, a tall enough tripod, and some willing labor to help get everything in position.

Indoors you might end up with a moderate wide angle lens, but pushing back and using a short telephoto, if practical, would minimize distortion.

I would certainly take the advice of Bozsik and get pictures of the labels, and the reverse sides whenever appropriate.

I feel you should apply what you know since its going into a book. Rather than stress about inside lighting, or doing things you're not familiar with and having a disaster, stick to your knowledge. For instance fold the quilts but display their pattern as they may be used outside. Spread them out among any patio furniture. You have a tripod so take timed shots (use your B). Indoors, you can still capture natural light. Pose the quilts within the available light and shoot away. people I feel are more concerned with patterns and layouts than they are with sizes as well. You can always say king or queen size but showing them how it will look in their possession is key, in my opinion.