An Interesting Thought...

[Statius]

I would say he would appoint the new recruits subsequently after:

1. fighting character
2. looks
3. size

He wouldn't buy slaves, that do not fit the criteria for the types he currently needs.
The problem with the fighting character is, that it is hard to judge just by looking at a person.

Unless you were a Retiarius one would say looks weren't too important a consideration as you would be helmeted for the duration of the bout.