Round vs. square:
A round pot will only hold about 78% as much soil as a square one the same size.
This gives
roots a little less room to grow in,
but if they do reach the edge, it is easier on them to make a gentle curve than the hard right angle they would encounter on a square pot.
For most seedlings in small pots, such as these, the standard nursery practice is to up-pot them at the same time that they develop their first set of true leaves. That practice
should eliminate the root-bound situation.
Small square pots may be a little easier to get the plants out - a putty knife makes a handy tool for sliding the seedlings out of the container.
Octagonal pots, I guess would be about half way between round and square. I've never used them. Sounds more like a marketing ploy to me. I would assume that they are more fragile than the square ones.
Because of the gentle turns of a round pot, they will suffer less cracking than the square ones, which means that you can probably
reuse them a few more times than the square ones.
Whatever size you use, just try to up-pot them before the plants get root bound. Stress on the roots at this stage of infancy will greatly effect the overall health/vigor of the mature plant. Pests attack the least healthy plants first. That is Mother Nature's way of culling. Survival of the fittest.