Here is a great resource for the right things needed to sew a swimsuit the right way. Basically, this delightful lady describes her trials, tribulations, and insights for sewing a swimsuit well. The main thing I will be using from her is the materials list and a few of the tips and tricks.
Fabric: 10% lycra, 90% nylon (aka: swimsuit fabric due to the necessity of recovery, which means how well a piece returns to the original shape. overall, you only need about a yard of fabric total to make a suit, though I'm planning on using a few different types of fabric, so that figure will be divided over the various fabrics.
Swimsuit lining: again, recovery is key to prevent the droopy saggy butt that some suits are plagued by. 1/2 a yard of nude colored lining will do, but I'm considering using Powermesh or Powerknit to help stabilize the top part and suck in my gut. Might end up cannibalizing a Spanx tank top I own that I never wear because it rolls up. Clipping the top to the bottoms might solve my rolling issue.
Thread: bulky nylon thread in either a coordinating color or contrasting color. Still have to decide on which color(s) I will need for this project.
Stretch or ballpoint needles: Schmetz 75-11 is recommended, but I only have a regular machine and will have to see what works with what I have.
Elastic: for arm and leg holes as well as possibly under bust, though I'm planning to use an existing bra and build upon it, so that might not be quite as important.
Old bra: Since I really need the support, I'm just going to use an old bra as a base for the swimsuit top, similar to this DIY, but with a lot more shaping over the cups instead of gathering in the middle.
Next up: drawing up something so I have a plan to follow and can make a pattern from things I already own.