@WalknOnEggShells, CC posters have produced some studies suggesting that good small LACs and universities do well in terms of getting kids into PhD programs (I think Reed and Swarthmore are particularly strong here). Some small schools are also good feeders to high-end professional schools (I think Williams and Amherst are particularly strong here.) So, I don’t think size of school needs to be an issue.
I agree with @ucbalumnus’s comments about making sure you understand what specific preparation is needed for what graduate program.