with the exception of the Roman numerals I have on my left wrist.

I've got seven of them. I still believe the industry sort of dictates what's "acceptable." However, once hired and depending n the nature of interactions, I suggest to keep them hidden when you can.

My team meets with a bunch of execs, leaders, and senior management types. These folks are sort of traditional (mainly government right now). So, I keep the tats to myself is how I feel. In a more modern office though, I've been more easily swayed to allow my arm tats to show when wearing short sleeves.

All that to say... Just be cautious of the overall environment and make the best decision from there.

Edit:

"The jobs in question aren't exactly high end. They're intermediate positions where I will be doing clerical/data entry and at times, provide customer support."

Remember that you could encounter many different people in a role like this one. And those people could help take you to another level if and WHEN you make the right impression (RESULTS; not ass-kissing) per se. I'd still say to hide them until you get a lay of the land.