You choose who to submit to. They then choose whether to represent you, but the first choice is yours. So, before you plough through the lists in the Writers and Artists Yearbook alphabetically, have a think about what you want from an agent and at least start with your first choices.
Things to think about...
A small agency (ie an agency with one or two agents, and therefore with proportionally fewer clients) is directly linked with the success of your career. You earn, they earn, simple as that. Your agent is more likely to be at the end of the phone for you or return messages quickly. A bigger agency may have so many clients (and probably administer the estates of dead authors) that the link is not as direct. This is good when it means they can afford to carry you for a number of years before you start earning for them (for example, if you're writing quirky or very literary work, something that may be harder to place than work that fits a commercial genre). It's also good because lots of big name clients means the agency has clout and publishers will avoid offending them. It's bad when it means you are the teeniest tiddler in their large and well stocked pond and have to struggle to get any attention from your agent because they're too busy dealing with their big fish clients. A big agency will also have in-house departments which cover areas such as television and film and foreign rights, although smaller agencies will have deals with other specialist agencies so that shouldn't be a major issue.
Agents have usually worked in publishing or bookselling before they become agents. In publishing they may have been in editorial or sales, marketing or rights. Those who are former editors usually have a particular interest in, surprise surprise, editing and may want to work on your book before sending it out to publishers. Agents from marketing/selling/rights backgrounds are less likely to want to edit but will be experts in their area. You may like the idea of editorial support, or you may not. It's a personal choice, but it's one you should think about.
A new agent will have lots of energy, but may not have either contacts or experience. They are more likely to be looking for clients. An older agent should have the contacts and experience, but might not be as enthusiastic about their 100th client as their first one. They will be looking to add to an existing client list so you have to fit into that list.
Always meet an agent before you sign with them. I've heard of agents offering representation without actually meeting their potential client and that worries me. It's supposed to be a business partnership. They're not going to be your bestest friend ever or your therapist but you have to get on with them and trust and respect them. Editors move around frequently so the relationship with an agent is likely to be the longest relationship in a writer's career.
Think about what you'd like ideally. You may be wrong or your ideal agent may, sadly, not be interested in you. But don't get into the position of writing to an agent asking for representation and then, when it's offered, getting cold feet. Think first, then jump.