Is a 1TB drive too big for a boot drive?

"Can the drive you choose to boot off affect performance?

It can affect it, but most likely in a positive way. Larger hard drives can be faster due to higher data density.

Would I receive faster boot/shutdown times if I were to choose a smaller drive?

Doubtful

How would partitions affect performance/boot speed? Assuming all drives are the same RPM, lets say 7200.

Depends on how you partition it, I'd recommend reading this great article by Mitch Tulloch on partitioning drives. He discusses partitioning techniques geared towards performance such as

having your page file on a different drive
using FAT32 for smaller partitions"