there is a difference in a beam supporting only an attic space and a beam supporting bedrooms. attic space for limited storage typically requires 20 pounds per square foot for live loads and bedrooms require 30 pounds per square foot.
a beam is sized based upon the loads it must support and the length of the beam. They can be of solid sawn lumber, engineered structural composite lumber and various metals such as steel and aluminum. There are however limits to the spans based upon their loads.
if a room is being formed in part of the garage then it may be possible to install a column within the new wall. shortening the beam spans will allow more options for your beam. the 2009 International Residential Code provides prescriptive beam design for solid sawn lumber. http://publicecodes.cyberregs.com/ic...9_5_par024.htm
engineered structural composite lumber manufacturers have prescriptive tables for their products. Some aluminum beam manufacturer's have prescriptive tables for their products. Typically steel beams are designed by a professional engineer.
Should you desire to add a second floor onto the garage I would recommend having a conversation with your local building official to determine what your building code is, what drawings will be needed, and other requirements.
Typically your foundation would need to be evaluated by a professional engineer to determine if it can support the added loads. Adding more load onto a foundation than it or the underlying soils can support could create structural issues. Footing size for foundation walls are based upon the loads they must support and the soil bearing capacity of the soil.
If you decide to move forward with this project I would recommend hiring a local professional engineer that specializes in residential construction. Just remember, not having a building code to build by, not needing a building permit, or are not required to submit drawings to the building department does not change the physics of building construction. The money you spend in having it designed properly will save you money in the long run, especially if something is overlooked.