Agree with the answers so far. If want to keep the academic door open, then in my opinion you need to fully commit to that and plan accordingly. The landscape in academia is far more competitive than industry these days. If you are ambivalent or non-specific about your academic aspirations you could quite easily get slotted into a postdoc job that doesn't set you up for academic success. If you do well in the academic sense and then change your mind and switch to industry little harm is done. The reverse is not true. I have seen many young scientists accept postdoc jobs who were not specific about their goals and ended up essentially working on other people's papers and grants and not carving out their own independent research as they need to. So, if you want a postdoc with potential to lead to an academic career you need to think about several issues.

1. Publication potential. This is the number one issue. Think about this a lot. What projects are getting started in the lab, that are very well-funded and likely to lead to high-impact papers. Unfortunately, you can't afford to just hope a great project comes your way or that you think of something great. Be very explicit about this. The ideal situation is that you get assigned to be the point-person, with clear authorship expectations, on a high-potential project.
2. Reputation of PI and Institute. This matters. Senior people (the ones deciding who gets what grants, jobs, etc) will say things like: He/she came from Dr. Famous' lab almost as often as he/she wrote that great paper. Also, these famous PI's will later be called on to write letters of recommendation when applying for training/transition grants, first position and later promotions in the tenure-track process. Therefore, you should be flexible about where you are willing to go. If the most famous lab in your area is in Wisconsin, or wherever then you should consider that location even if its not where you imagine settling down.

So, how to get a position that meets the above criteria. Cold-calling is almost hopeless. It doesn't hurt (except the time it costs) but will have a very low success rate. The top people at the top institutes as described above don't need to advertise and don't have time to find your email/call in their inbox/voicebox. They will most likely hire the "brilliant postdoc" that their old friend or other famous PI recommends to them. Therefore, your own PI, committee members, and any other people in the field that you know are the best source of potential connections to get interviews. Make sure that your CV and online presence are in excellent condition. Getting active on blogs/forums talking about your recent publications might not hurt. Applying for funding is an excellent idea. If you have a fellowship that is a huge draw for most labs even those that can afford to pay you. Current funding is the best prediction of future funding. Missing any level will hurt you and you will have to work even harder to get back on track.

If you follow all of the advice above and after a few years the prospect of the academic rat race is not growing on you, you will still be relatively well positioned to switch over to industry. If you know for sure that academia is not for you then I would probably adopt a slightly different strategy and focus most on acquiring the skills most sought by industry. At the moment general experience with genomics and especially informatics will be sufficient but who knows what the future holds.

Nothing will beat having your own source of funding. Such fellowships/grants/awards do exist but are highly competitive.

Failing that, be honestly interested in their work.

1. Talk about some published work by them that has inspired and excited you.
2. Talk about what you wish to focus on if you were offered a position in their lab.
3. Tell them what you can bring to the table in terms of the skills you have that will help them get their next paper.
4. Figure out what skills you would like to learn while in their group to further your own research career goals.

I think what you should look for in a potential post-doc position depends largely on what your career goals are. Why do you want to do a post-doc?

If you're interested in Academia (being a professional grant writer) you should (therefore) be writing grants and getting your own funding. If all you're specifically interested in learning a new area (such as ChipSeq) to jump start you in industry, then you may be more of a technician-type post-doc.

I think you'll be more desirable if you are clear with potential employers (post-doc advisors) what skills you bring to the table and what you want to get out of the relationship. A hiring PI will want to see proof of what you can do (best conveyed as publications, but good recommendations can go a long way also).

As someone who both advises students on postdoc opportunities and evaluates prospective postdoc applicants, I have four bits of advice for you:

1. Find candidate labs that can support you in your career goals. Decide what it is that you want to do after your postdoc (in as much detail as you can), then determine what skills/expertise are missing, then find a lab that will move you closer to your goal. That could mean learning a new technique, or exposure to a new area of science. It could mean learning from someone who's done startups, or someone who's mentored people to tenure-track positions, or someone who has good contacts in big pharma.
2. Craft a good cover letter. If you decide to apply to 10 labs, sending the same CV is perfectly fine. Sending the same cover letter to all 10 is almost guaranteed to be a failure. I'd estimate that 75% of applicants to my lab send a stock cover letter, and 95% get a form letter rejection in response. Of the 25% of applicants that have a good cover letter, 50% get some sort of follow up from me. What makes a good cover letter? Answer two questions: how do your skills and interest match my lab's research, and how does a postdoc position in my lab serve your long-term plans?
3. Don't just apply to posted ads. All sorts of reasons for this: existing students/postdocs may be on the verge of leaving, or money could be on the verge of arriving, or your skills could be such a good match that the PI can figure out how find money. But you don't know if you don't apply.
4. Be persistent (a little). PIs are busy, and they don't always get things promptly. And sometimes they slip under the radar. A follow-up email after two weeks is perfectly appropriate, and it shows that you are definitely interested.
5. (bonus) Ask your current adviser to proactively send a letter of reference. Obviously you should only do this if you have a great relationship with your adviser, and you should only do this for positions you're really excited about. But if your current adviser is raving about you, then it's hard for me not to at least set up a phone interview with you.

Good luck...