Efficient uptake of prey and nutrients from the environment is an important component in the fitness of all microorganisms, and its dependence on size may reveal clues to the origins of evolutionary transitions to multicellularity. Because potential benefits in uptake rates must be viewed in the context of other costs and benefits of size, such as varying predation rates and the increased metabolic costs associated with larger and more complex body plans, the uptake rate itself is not necessarily that which is optimized by evolution. Uptake rates can be strongly dependent on local organism geometry and its swimming speed, providing selective pressure for particular arrangements. Here we examine these issues for choanoflagellates, filter-feeding microorganisms that are the closest relatives of the animals. We explore the different morphological variations of the choanoflagellate $Salpingoeca\; rosetta$, which can exist as a swimming cell, as a sessile thecate cell, and as colonies of cells in various shapes. In the absence of other requirements and in a homogeneously nutritious environment, we find that the optimal strategy to maximize filter-feeding by the collar of microvilli is to swim fast, which favors swimming unicells. In large external flows, the sessile thecate cell becomes advantageous. Effects of prey diffusion are discussed and also found to be to the advantage of the swimming unicell.