What are the common types of leukemia for a 25 year old?

Several... It's difficult to say in just a few words but, generally speaking, at young ages, leukemias are more likely to be of the acute rather than chronic type. In terms of cell of origin, they can be lymphoid or myeloid, so most of the time at this age it will be acute lymphoid (lymphoblastic, all) or acute myeloid leukemia (aml). Chronic myeloid leukemia (CML) is also possible but not as common.
Leukemia age-wise. Acute myeloid leukemia, chronic myeloid and chronic lymphoid leukemias are most common in adults but are of highest incidence after 50 years old (7-9th decade). Children less than 15 years old have higher incidence of acute lymphoid leukemia. The incidence of any kind of leukemia may be at its lowest for the age group 15-29.