You have two issues to consider.
One: The best way to get an interview.
Ask the recruiter for advice and help. If you make direct contact with a hiring manager, ask that person for help too. "I really want to work here; please help me make that happen" is a good way to pursue it.
Two: Conflicts between recruiter and hiring company
This really isn't your problem, but still be sensitive to it. As a hiring manager I've had a few hassles about whether recruiters should get paid when I got a resume from more than one source.
Here's the thing: Commission recruiters get paid when a candidate they present gets hired. So, if they present your resume first they'll be entitled to get paid even though you sent your own resume later. You can be transparent about this by putting a note on your resume saying "Jack Sprat of the firm Abc told me on (date) he would present me for this job.)
If you have a friend present your resume to get a referral bonus, but a recruiter presents you first, your friend probably will not get the bonus. Let your friend know about this.