Summer Internships or Graduate Programmes?

Okay, so I'm a third (final year) target uni student without any relevant experience/internships. All I have is insight days/2 weeks experience as a financial analyst in industry which was very unrelated. I just want opinions on whether I'm doing the right thing by applying for summer internships for next year saying I'm going to do a Masters (making me a penultimate year student), as opposed to applying for graduate positions straight up.

Is this a legit plan even if I went on not to do a Masters? And also do you think it's a good idea to apply for a combination of internships and grad positions, i.e. internships at BBs, top boutiques etc and grad positions at MM firms, or will I get outright rejected from MM firms without related experience also?

Thanks in advance.