Is it better to do an internship that can give you more connections or one that is more relevant to my major?

First and foremost, any Internship is a wonderful opportunity (and a MUST to build a qualified resume as you prepare for a full time position). So just by planning to take on an internship (or internships) you are already doing something very valuable and the "future you" will thank you for it!!! You will receive valuable experience interacting with others on a team and those in leadership roles as well. You will learn how to multitask, work against deadlines as well as interacting with different personality types. For business as a whole, general internships are absolutely fine. If you are considering a specialty (such as technical engineering, coding, research in a specific field, etc.) then I would recommend taking a more targeted approach and look within those fields. Otherwise, there is no bad Internship opportunity if it can help you learn more about the world of business and the wheels that move it forward every day! Be curious, be positive and be gracious (and show gratitude) - those traits will move you forward every time!!!

It's hard to answer this without knowing more about your situation.

But in general your internships should be about making connections and expanding your network. You want your internship supervisor to introduce you to lots of people.

I would say anything that gives you relevant, tangible experiences that will translate nicely onto a bullet point on your resume! Many times its your work that needs to speak for itself before another person can go to bat for you. Work hard and those connections will follow!