Using the deep multi-wavelength MUSYC, GOODS, and FIRES surveys we construct a stellar mass-limited sample of galaxies at 2<z<3. The sample comprises 294 galaxies with M>10^11 Solar masses distributed over four independent fields with a total area of almost 400 sq arcmin. The mean number density of massive galaxies in this redshift range is (2.2+-0.6) x 10^-4 Mpc^-3. We present median values and 25th and 75th percentiles for the distributions of observed R mags, observed J-K colors, and rest-frame UV continuum slopes, M/L(V) ratios, and U-V colors. The galaxies show a large range in all these properties. The ``median galaxy is faint in the observers optical (R=25.9), red in the observed near-IR (J-K=2.48), has a rest-frame UV spectrum which is relatively flat (beta=-0.4), and rest-frame optical colors resembling those of nearby spiral galaxies (U-V=0.62). We determine which galaxies would be selected as Lyman break galaxies (LBGs) or Distant Red Galaxies (DRGs, having J-K>2.3) in this mass-limited sample. By number DRGs make up 69% of the sample and LBGs 20%, with a small amount of overlap. By mass DRGs make up 77% and LBGs 17%. Neither technique provides a representative sample of massive galaxies at 2<z<3 as they only sample the extremes of the population. As we show here, multi-wavelength surveys with high quality photometry are essential for an unbiased census of massive galaxies in the early Universe. The main uncertainty in this analysis is our reliance on photometric redshifts; confirmation of the results presented here requires extensive near-infrared spectroscopy of optically-faint samples.