As Stuperman has suggested, it's all about creating armies centered around HA's (with cataphracts as support as soon as you can get them). Also, the Persian Cavalry (HA unit) will give you some measure of melee value.

Hillman and Eastern Infantry are arguably the most worthless infantry in the entire R:TW world. Still, they are effective in their use as "bait". Encircle and then rain down arrow upon arrow on your enemy forces as they approach your main battle line. If all goes as planned, you'll witness multiple enemy units routing prior to engagement with your infantry.

Be forewarned however, Hillmen or Eastern Infantry will run if the sun goes behind a cloud or an enemy combat unit approaches them and says "boo". Hire mercenaries when you get to other regions.

Careful management of finances in the early going is key to success when playing Parthia. Acquire provinces with sea ports as soon as possible - AND - avoid conflict with Egypt and to a lesser degree Selucia for as long as you can.