All of this is intelligent advice being given by intelligent people, so I would take note of it, Scott.
Equally, however, I think it is answering a slightly different question to the one that you asked, which is for recommendations, rather than the details of how you actually go about applying to an agent.
In this respect, I am afraid, there are no easy answers again: the simple truth is, finding a good agent is a matter of trial and error because different sorts of agency suit different types of actor, and you have to work out what will function most appropriately for you. There is, naturally, a consensus that certain agencies are the best in the country - and they undoubtedly are, because they represent the biggest names working within the industry, have the most wide ranging contact bases within both the national and international markets, and, most importantly, generate enough leverage to get their clients seen for prestige projects. By and large, they will not even look at you unless you are already making some serious headway into the industry as a whole. But it is also true that their client base is huge, and many lesser actors, who have been taken on in a momentary fit of enthusiasm, get lost amongst the campaigning to get big-name stars big-name parts. This may mean that being with a huge agency is not, initially, as beneficial for you as being promoted by a smaller scale agency that can actually match jobs to your skills base and industry standing, and realistically get you seen for parts (as well as treating you as an individual, and helping you to define your own career path).
The questions you need to ask yourself when winnowing out agencies are:
a) Where do you see yourself being based? I know you've said that you aren't based anywhere at the moment, and that your home life may be in flux, but this is not a helpful attitude. Try and work out either where you are likely to/want to settle, and search for agents in the locality. There is very, very little point in being represented by someone who operates miles away from your home base, because there is no easy way to communicate with them when you need to, and your agent needs to be accountable to you, to a large extent.
b) Ask yourself what sort of agency you are interested in being taken on by: would you prefer to try and push for representation by a large conglomerate (unlikely though you may be to be seen initially?). Would you prefer a smaller bespoke agency? Would you be prepared to work in a co-op and promote yourself (and others?). Have you got special skills that a particular agency caters for better than another?
c) Are you particularly proficient in certain types of performance and genre? If so, can you find agencies where it looks as if the clients are being promoted for the same sort of work you would be interested in finding (you can find this out by accessing client CV's and reading news pages on agency websites?) This is important because some agencies have very specific networks of contacts that are a great match for certain types of actors, and hopeless for others. Be realistic about this: I have no skill in musical theatre, and therefore avoid conspicuously anyone who primarily promotes musical theatre actors; similarly, I know I am a character actor, and that certain agencies will not promote someone who is 'characterful' well, just as, in the same way, you don't wish to be a leading type actor who is represented by a character actor dominated agency. Many agencies have deliberately mixed representation, so that the clients cover a wide spectrum of casting possibilities, but they still tend to specialise in getting higher ratios of commercial work, musical theatre or theatre, Internet broadcasting etc. depending on the agency contacts. It is worth trying to analyse the calibre of an agency's current clients as well, if you can, and seeing if you think your skills are a good match for theirs, as it's too easy to pitch yourself at too high or too low a standard within the industry, and ensure no-one takes you seriously.
d) As Helen says, all the time be on the lookout for shysters who are attempting to make a quick buck from you. They are sometimes a little difficult to tell from serious agents at first, and just because an agency is a new setup (CCP will tell you when an agency was founded) doesn't mean it won't prove to be any good. All you can say here is that a brand new agency may be more 'hungry' to get its clients work, but has not really been tested in the market so may also fold at a later stage if it cannot generate enough work from its clients. Older agencies are more proven (though they still get bankrupted, close shop etc. from time to time). The things that guarantee an agency is shystering you, however, are: any request that you pay an upfront amount of money to be placed on the books or have in-house photographs taken to promote you and an undue emphasis on signing any binding contract that demands you to be tied to the agency for an extended length of time (say, a year - a more general contract laying down the agents obligations to you, percentage commission rates and terms for leaving the agency is more acceptable - but many of the highest ranking agencies seal a deal with no more than a gentleman's agreement between you that you will work to the basis of a verbal agreement between you in each others' best interests).
Many actors complain about the way in which agents will take a cut from any work you do, even if you found the work for yourself, although in my experience, if the work doesn't pay well in the first instance, a decent agent tends to waive the cut, preferring to see you working. Some agents can be quite doctrinaire about what work you take on and what work you shouldn't be seen to be doing. Neither of these things is considered untoward, or the mark of a bad agent, though they may not suit you personally, and you may have to keep searching to locate an agent with whom your dealings feel comfortable. However, you should always avoid signing up to e.g. directory websites in lieu of finding an agent unless you are fully prepared to accept that what you are doing is paying a fee with no guaranteed work at the end of it, and a partial expectation that you are selling yourself. There are many such websites that masquerade as 'agencies' when, in fact, all they are doing 'on your behalf' is hosting pictures and profiles of you that casting people may happen across once in a blue moon. This is not agenting in anyone's book, but people who are signed solely to directory websites sometimes wish to imply that they are 'represented' by the website. Don't fall into the trap - the only usable websites are the ones that allow you to apply for jobs on your own behalf.
e) As everyone has said, this may all be somewhat pre-emptive, anyway, as you may well need to get a much more solid body of work/experience behind you before agencies start being interested (after all, they want to think you can make them money). But it is all good advice that is worth considering well into the future.