Switching to a more expensive tire with better rolling resistance would probably make a bigger difference than just tire size.

I'd recommend a Continental gp4000 in 28c:
http://amzn.com/B00G8QGVPS

I've read that they run small, so I think a 28c (their "largest" size). The gp4000 is as close to a race tire as you can get without losing puncture protection. (I mean a 25c would probably be fine to).

Ideal tire size for speed depends on your weight. Like a 250lb rider is going to be faster on a "bigger" 25c tire than a smaller 23c tire. Whereas a light 120lb rider would probably be the fastest on a 23c tire.