Not going to be much difference (if any) between 31 and 30 inches. You'll find more difference between two different manufacturers. Winegard's 76cm (30"), for example, often outperforms more poorly made 36" dishes. Generally, though, bigger is better.
You'll see a significant increase in performance between 30" and 1 meter.
Everything else being equal, the lower the noise factor of an LNB, the better. A .3 will outperform a .6, for example. However, noise factor isnt the only important specification. L.O. (Local Oscillator) stability is equally important, although most consumer LNBs have similar L.O. stability (+/- 1 Mhz). I have a commercial Norsat PLL LNB that has a .9 noise figure but a L.O. stability of +/- 100 Khz which performs comparably to an Invacom .3.