Yeah...forgive me if some of my stuff is off (I didn't play past AD&D 2nd edition rules), but I'd try and match up existing weaponry that they have damage, speed and range factors for, and use that for the Greek and Roman Weapons.
As a class, you may want to give certain ability bonuses or skills due to their regimented and disciplined trianing, such as saves vs. certain attacks (maybe poison, sleep, paralyzation) and that type of thing. Bonuses maybe to hit and damage for fighting in a group vs single. Or, give a defense bonus when more than one tower shield (scutum) is employed, especially against ranged weapons. Also maybe give a bonus to morale or innitiative to the greeks or romans when deployed in formation. You could also give bonuses to fear saving throws when in formation.
The shortsword is a tough one...I think the base damage was 1D6 right? To me that's always been stupid...the damage should be the same as a long sword, just the range is less, or make it 1D6+1 or something. Especially the way a shorter, thick blade can cleave.
I'd also have special rolls for pilum effects...such as shield penetration for an extra 1d4 damage to the defender (for those with shields), and a % chance of the shaft breaking so it's not useable next time.
If i were you, i'd just start at the top...maybe begin with their gear and see if there are any characteristics that stand out and need to be addressed, like i mentioned above. I'd also maybe give +1 bonuses to constitution (due to legionary and hoplite endurance training), and for concurent levels, add bonuses to hit and damage with certain weapons. You could also grant certain skills once they achieve a certain rank, which gives anyone fighting with them bonuses to saving throws or to hit, or innitiative.
I miss D&D...