I'm careful to keep my hands off of the syringe walls for that reason, but I can see how it's an issue as several of my older syringes have had the markings start to rub off. You could put a thin layer of clear tape over them when new, although do it right the first time as peeling the tape off probably won't help the label.
When you buy the reagent refill kits they come with new syringes.
I know McMaster Carr sells them (although labelled in "units" as they are actually diabetes syringes, 1 unit = 0.1 ml). Farm stores if there are any remotely near hear routinely sell them. Honestly if there's a needle exchange clinic somewhere they'll probably have them. I'd avoid pharmacies though. Although a different state last time I tried to get a leur lock syringe (not even needles) at a pharmacy it started resulting in "Can I see your driver's license?" and an employee going for a phone.