Molecular dynamics simulations are used to study the equilibrium properties and collapse dynamics of a heteropolymer in the presence of an explicit solvent in two dimensions. The system consists of a single copolymer chain composed of hydrophobic (H) and hydrophilic (P) monomers, immersed in a Lennard-Jones solvent. We consider HP chains of varying hydrophobic number fraction n(H), defined as the ratio of the number of H monomers to the total number of monomers. We also consider homopolymer chains with a uniform variable degree of hydrophobicity lambda, which describes the hydrophobic-solvent interaction, and which ranges from hydrophilic (lambda=0) to hydrophobic (lambda=1). We investigate the effects of varying n(H) and lambda, the HP sequencing, and the solvent density on the equilibrium and collapse properties of the chain. For sufficiently high n(H), we observe a collapse transition for random copolymers from a stretched coil to a liquidlike globule upon a decrease in temperature; the transition temperature decreases with increasing n(H). The transition can also be induced at a fixed (and sufficiently low) temperature by varying n(H) for random copolymers or lambda for homopolymers. We find that polymer size varies inversely with solvent density. The rate of polymer collapse is found to strongly vary inversely with increasing n(H) and lambda for copolymers and homopolymers, respectively. Further, the collapse rates for these two cases are very close for n(H)=lambda, except at lower values (n(H)=lambda approximate to 0.5), where the homopolymers collapse more rapidly. At moderate densities (rho=0.5-0.7, in LJ reduced units), we find that random copolymers collapse more rapidly at low density and that this difference tends to increase with decreasing n(H). At fixed solvent density and n(H) we find the collapse rate differs little for random copolymers, and multi-block copolymers with equal n(H). Finally, the simulations suggest that copolymers tend to collapse by a uniform thickening rather than by first forming locally collapsed clusters which aggregate at longer time. The exception to this appears to be block-copolymers comprised of sufficiently long alternating H and P blocks.