Would my arm tattoo be a problem?

It would be silly for me to make a generalization about an entire set of industries, but I can tell you the impressions I've gotten from my own experiences. I would say few people you encounter, if any, would care at all. Not having seen the tattoos, I can't be certain, but from what you say, not a big deal.

Most likely a complete non-issue. I've worked with engineers at companies headquartered here in SF Bay Area, East Coast and Europe, many of whom have one or multiple tattoos, and they have not faced any difficulties. That said, for any professional careers, I'd recommend against neck, face or finger tattoos.

I have an entire arm sleeve of tattoos and I have not found it to be an issue in my job working in the tech industry. There are times and important meetings with executives where it may be appropriate to cover up with long sleeves. However, I've found that people are going to judge you by your work ethic and quality of performance, not based on what may or may not be tattooed on your body. Tattoos are very common in the workplace these days and if an employer is going to be judging your for them I think that speaks to larger issues around their company culture.

I think this is going to depend on which career path you choose to follow and the types of organizations you plan to join.