I was thinking of applying for internships over the summer, and I was trying to determine if I should include the regional airlines in that search?

is an internship at a regional airline a good idea? will it be beneficial in my future endeavors both at a regional and trying to apply for a major?

Intern at a place you would like to retire.

I did a summer internship in the summer if 2008 in flight ops for a regional carrier. You will lose time building time, however, it saved my bacon during the recession. I graduated immediately after the summer internship and regionals were shedding pilots left and right. I was able to use my internship to get a non-flying job. While my buddies were laid off, I was still able to bring home a paycheck.

Side note: Due to unrelated issues, I am currently not flying, but again, my internship opened those doors that otherwise would have been closed

I think the best option would be a major career. At the same time though an internship is better than no internship. I would to all the places you wouldn't mind being an intern for, then pick which one you want to go to. I did the Continental internship in 2010 I haven't seen the effects so much but it was one of the most fun experiences I have had.

In short an internship with any carrier will not hurt.

I did mine with a major and was offered preferential hiring with a regional affiliate. A friend of mine interned with a regional and got offered preferential hiring at that regional. Basically, just because you interned for a major, don't expect it to allow you to skip the regionals.