There are generally a broad merchant opportunity for either sale as Pets, or for Laboratory use.
In the class as Pets it could be mice and rats; usually the gerbil does well; but also there is a more seasonable market for creatures like rabbits. In the case of rabbits and chickens there can be a secondary market to food vendors. The thing to do is make an estimate of just how involved you can manage, needing food, space, and cleaning. Investigate at local pet shop to learn about works in your area.
The other major category can become quite an industrial process, as that Labs want assurance of animals health and age. Typically they order all white-mice. An example of this industry can be located by the name Blue Spruce Farms, of Altamont, New York.
A lot of reptile owners purchase mice, pinkys, and fuzzies. So I would probably breed mice.
What rodents would be the best for me to begin breeding and selling? I'm meaning money and popularity wise. I can handle raising them just fine.