Glycolic acid and glycine can potentially self-oligomerize or co-oligomerize in solution by forming ester and amide bonds. Using density functional theory with implicit solvent, we have mapped a baseline free energy landscape to compare the relative stabilities of monomers, dimers, and trimers in solution. We find that amide bond formation is favored over ester bond formation both kinetically and thermodynamically, although the differences decrease when zwitterionic species are taken into account. The replacement of ester linkages by amide bonds is favored over lengthening the oligomer, suggesting that one route to oligopeptide formation is utilizing oligoesters as a starting point. We also find that diketopiperazine, the cyclic dimer of glycine, is favored over the linear dither; however, the linear trimers are favored over their cyclic counterparts. Because glycolic acid and glycine are dominant products from a Strecker synthesis starting from formaldehyde and HCN, this study sheds light on potential pathways to prebiotic formation of oligopeptides via oligoesters.