Gas-giant planets that form via core accretion might have very different characteristics from those that form via disk instability. Disk-instability objects are typically thought to have higher entropies, larger radii, and (generally) higher effective temperatures than core-accretion objects. In this paper, we provide a large set of models exploring the observational consequences of high-entropy (hot) and low-entropy (cold) initial conditions, in the hope that this will ultimately help to distinguish between different physical mechanisms of planet formation. However, the exact entropies and radii of newly formed planets due to these two modes of formation cannot, at present, be precisely predicted. It is possible that the distribution of properties of core-accretion-formed planets and the distribution of properties of disk-instability-formed planets overlap. We, therefore, introduce a broad range of "warm-start" gas-giant planet models. Between the hottest and the coldest models that we consider, differences in radii, temperatures, luminosities, and spectra persist for only a few million to a few tens of millions of years for planets that are a few times Jupiter's mass or less. For planets that are ~five times Jupiter's mass or more, significant differences between hottest-start and coldest-start models persist for on the order of 100 Myr. We find that out of the standard infrared bands (J, H, K, L', M, N) the K and H bands are the most diagnostic of the initial conditions. A hottest-start model can be from ~4.5 mag brighter (at Jupiter's mass) to ~9 mag brighter (at 10 times Jupiter's mass) than a coldest-start model in the first few million years. In more massive objects, these large differences in luminosity and spectrum persist for much longer than in less massive objects. Finally, we consider the influence of atmospheric conditions on spectra, and find that the presence or absence of clouds, and the metallicity of an atmosphere, can affect an object's apparent brightness in different bands by up to several magnitudes.