We use broadband photometry extending from the rest-frame UV to the near-IR to fit the individual spectral energy distributions of 63 bright (L(Ly{alpha})>10^43^ erg/s) Ly{alpha} emitting galaxies (LAEs) in the redshift range 1.9<z<3.6. We find that these LAEs are quite heterogeneous, with stellar masses that span over three orders of magnitude, from 7.5<log M/M_{sun}_<10.5. Moreover, although most LAEs have small amounts of extinction, some high-mass objects have stellar reddenings as large as E(B-V)~0.4. Interestingly, in dusty objects the optical depths for Ly{alpha} and the UV continuum are always similar, indicating that Ly{alpha} photons are not undergoing many scatters before escaping their galaxy. In contrast, the ratio of optical depths in low-reddening systems can vary widely, illustrating the diverse nature of the systems. Finally, we show that in the star-formation-rate-log-mass diagram, our LAEs fall above the "main-sequence" defined by z~3 continuum selected star-forming galaxies. In this respect, they are similar to submillimeter-selected galaxies, although most LAEs have much lower mass.