Another vote for Karen Kay Buckley's Perfect Circles. I just set them on the fabric, do a running stitch around the edge & pull. Then, I "paint" on some liquid starch with a Q-tip or clean paint brush and press. Once I have the circle shape, I pull out the circle template & press again.
It's possible to make your own templates using the Mylar template plastic (I buy it all the time at JAF for my other templates), but the trick is trying to cut a perfectly round template out of plastic. It ends up involving way too much marking, trimming & sanding for it to be worth my time. The pre-cut perfect circles are well worth the investment. I bought mine at a LQS & don't remember the exact price, but it was quite reasonable.
I personally love doing needleturn applique, but I fudge it a bit with the circles & do turned edge applique, attached by hand, because trying to turn under a perfect circle while I'm stitching is way too frustrating. I also tend to glue baste the circle down in the center so it doesn't shift on me while I'm stitching it. Typically, I would use applique pins, but I find just a small dot of glue (I like the Glue Baste It! EZ squeeze bottle by Roxanne's because I can perfectly control how much glue comes out, but I think any water-soluble glue would work) will hold it nicely & the results are beautiful every time.
If you're going to machine applique them, I agree with Murphy that you want to apply fusible web to the back of your fabric & then cut it out to the exact size using a die cut machine. With fusible, you want to be extra careful to match your needle size to your thread size. For example, with Aurifil 50/2, I'd use a size 70 needle because it is a very thin thread. If for some reason you want a more decorative finish & are using a larger thread, like a 28/2 or 12/2, size up to a 90 needle. I probably would not recommend a size 40/2 thread as it will not lay as nicely on the edge & will not puff up enough to look decorative either.
Can't wait to see a photo of your finished quilt! It sounds lovely.