Include what's terrific about you, what your successes have been, and why any search firm would be blessed to have you in their stable of prospects. You can't afford to seem squishy, tentative or lacking confidence with any of the leads that might come your way. Check in with both your undergraduate and your graduate school career and alumni offices for names of other alums working in executive search. Call or write them asking if you could have 20 minutes of their time to get a better idea of how they find their prospects. You never know when one of them will volunteer to help.
Contingency is more like a crap-shoot, with lots of guys trying to hit a moving target.
I'd stay open to both. Once you have your Kennedy's listings in hand, you can locate firms by location and industry, and consider sending them your resume. I guess it's hard to argue with that. Just be sure nobody floats your name out there without your permission, however. Check out sites on the Web that offer a search firm capability.