Sizing of a beam requires estimating the loading on the beam. In your case, you state you are storing "misc stuff", so you need to estimate the weight per square foot of the "stuff". Just to get you started, light "stuff" like bags of styrofoam might weight up to 10 pounds per square foot. Heavy stuff like books or magazines weight approximately 50 pounds per cubic foot, so if you are planning to stack the "stuff" a foot high, that would be about 50 pounds per square foot, or if you were planning to stack paper 2 feet high that would be 100 psf. If you are planning to store machinery, tools, steel pipe, or similar "stuff", you could easily get up to 150 psf.
The size of your beam will be determined by the loading of the "stuff" you are planning to put up there. It will also be determined by the fraction of the total area of the loft to be supported by your beam, which will be determined by the geometry of your mezzanine, which you can show us via a detailed plan.
So once you specify the loading and the geometry, it is possible to size the beam.