Seon, a good rule of thumb to follow is: Don't guess!!! Strength of beams has more to do with the web thickness and height than anything else. If you go with half the height, you cut the strength by a factor of 4 or more.
If you plan on supporting the beam only on the ends, you design for DEFLECTION that you can tolerate, not the bearing capacity of the beam. Sure, you can load a beam at 700 lbs per foot, but on a 20 foot span you will get 3 inches of sag in the middle. No good for actual building a floor on.
If you tell me your support, your span, and what kind of load you want to put on it, I'll tell you what size beam you should get and how much it will sag between supports. In the end, if you are going to build with a permit, you are going to have to get a structural engineer to stamp a drawing anyway to get it to fly with the inspector. Also, when fire hits, steel beams tend to turn to butter and lose a lot of strength. Just something to keep in mind.
