If you have tried to purchase knit fabric you will have discovered that it is an absolute minefield. Fabrics are named/labeled according to a variety of combinations of fiber content, construction method, trademark/brand names, and my personal favorite, not at all.
So, first up, check out the graphic below for a quick run down on the basic construction methods and how to identify them.
The fiber content of the fabric affects the look and feel of each of these types of fabric dramatically, and each type comes in an endless variety of fiber content variations.
What you choose here is largely down to personal preference. The main thing that will affect the success of your project, however, is the stretch and recovery of the fabric you are using. This can be estimated from the fiber content and construction method, but the easiest way is to do a simple stretch and recovery test on the fabric itself.
Knit fabrics can be either 2-way stretch (which means that they stretch from selvage to selvage but not along the length of the fabric), or 4-way stretch (stretches from selvage to selvage as well as down the length of the fabric). It is easy enough to tell if your fabric has 2 or 4-way stretch by stretching it in each direction. But how stretchy is stretchy? Fabric stretch and recovery, which means how well it bounces back after you stretch it, is measured as a percentage. You can find a full tutorial on how to measure the stretch and recovery percentages of your fabric here:
Stretch Factor - How to work out a fabrics stretch percentage
Shoot over and check it out and then you should be all ready to go with knits.
If you are ordering online it can be hard because stretch percentage and recovery are often not mentioned and can make or break a project, but you can get around that by ordering a swatch. Most online fabric companies will send you a swatch for a small fee and then you can test the fabric out for yourself. Once you have ordered from a particular store you will come to know the weight, stretch and drape of the fabrics they stock and you will be able to order next time with confidence.