There are two main types of thread for the bobbin, cotton and Polyester, both are great but each has slightly different characteristics.

Cotton
Quilters love it. It keeps the fiber content consistent with the fabric, batting, and top thread. Not such a favorite of the embroiderers, it is OK, but on dense fill designs, cotton bobbin thread will result in a stiff design.
It is very important that you choose good quality cotton for the bobbin. The lower quality cottons will produce more lint which in turn requires more frequent machine cleaning. Good quality cotton will produce little lint and less machine downtime.
Egyptian top quality extra long staple cotton fibers will give you very little lint. It is more expensive than a normal 100% cotton thread but both you and your machine will notice the difference when using this thread in the bobbin.
There are two types of polyester underthread, Spun Polyester and Filament polyester. Both work fine, here's some information about them both.

Spun Polyester
Spun polyester is very widely used, more than cotton because of its strength. Many sewers like this thread because it is stronger than cotton. Like cotton, it does not have a slick surface and it may very infrequently grab the top thread too tightly creating uneven stitches and top thread breakage. It is a good, inexpensive very popular under thread that will balance out any top thread being sewn.

Filament Polyester
A filament polyester underthread has a shiny appearance and is virtually lint free. It can be thin and lightweight, yet strong. Embroiderers love this thread over and above all the others because it creates a soft backing, even on dense designs with many machine quilters liking it due to its smooth surface.
A filament bobbin thread works exceptionally well with all threads, balancing them perfectly, it is also the underthread of choice if you are using metallic threads or heavy cotton threads. The smoothness of the filament poly thread does not snag or grab the top thread. If you've had trouble using metallic threads or heavy cotton threads, a smooth bobbin thread may solve some problems.

Pre-wound bobbins
Frequently Asked Questions about Pre-wound Bobbins:
1. Why use pre-wounds when I can wind my own?
The pre-wound bobbins are wound by high tech machines which provide a smooth, uniform wind. The result is much more thread on the bobbin than a self-wound bobbin. Having to stop in the middle of a project to change the bobbin is always an inconvenience.
2. Should I tear off the cardboard sides?
If the bobbin fit is too snug to accommodate free rotation, take off the cardboard sides. This will not affect the function of the bobbin. If your machine has an automatic bobbin sensor, leaving on the cardboard sides will make the sensor think the bobbin is always full and will therefore not provide a low bobbin warning. The solution is to tear off the cardboard sides and use the sensor, or leave the sides on and sew until the bobbin thread runs out.
3. Plastic or Cardboard sided bobbins?
Either type is fine. Plastic bobbins are reusable; cardboard bobbins are disposable. Because the plastic-sided bobbins are so smooth, they may continue to spin even after your machine stops and cause backlash. Some machines seem to work better with the cardboard-sided bobbins because the cardboard sides provide more friction and backlash is usually not a problem. If it is, the bobbin tension may need to be tightened.