First up, are you looking for a big agency or a small one?
The pros of a big agency are increased clout - very handy in these uncertain times - in-house specialist departments, usually handles big names and author's estates, so can take risks on some new comers. Cons are you'll be a little fish in a big, big pond and they may be relaxed about you making money as your income is less closely connected to their income overall.
Pros of a small agency are, you really matter to them so you're more likely to get personal attention, cons, they may not be able to carry you for any length of time if you hit a rocky patch, they may not have as much clout with publishers, they almost certainly won't have in-house specialisms - although they should have deals with specialist agents, so this won't matter too much.
Secondly, the experience and background of an agent. If they're new then they're likely to be hungry for success and work extra hard for you. On the other hand, they're unlikely to have the connections or clout of an established agent. If they're established, they'll have the connections and clout, but they're possibly less hungry and will have established clients to pay attention to first. The ideal is perhaps a new agent in an established firm.
Then there's the agent's own background. Usually they've come from either editorial or rights. Their approach will reflect this. My own agent has a background in rights and is a demon at selling them, but I think she'd be happy for me to say that she doesn't want to do much editorial work. That suits me, but it might not suit you.
Finally, there's personality. Do you like them? They're not going to be your best buddy-roo, but there should be mutual respect within a professional relationship.
Having decided what sort of agent you want, then how do you find them? And I'll do that tomorrow.