@Holumpa I've been working on writing and illustrating and also have a full-time job, so I'm really only interested in taking on a small amount of projects a year and would like them to be children's books. While I'm open to other opportunities (I wouldn't turn down an opportunity to work on a board game) I don't need to fill my schedule with smaller projects to pay the bills. Because of this, a literary agency was the best fit for me (as opposed to an art rep). So I started by locating literary agents who repped illustrators as well as authors.
I then narrowed it down to small-to-mid-sized agencies. This is just my personal opinion/impression from listening to podcasts and looking at social media but it seems like slightly smaller agencies have a little more time to highlight and focus on each author/illustrator they represent and I liked that. There are pros to larger agencies as well - they have more visibility and can maintain larger networks than smaller agencies.
After that, I looked into the artists and writers currently on each agent's list. I was looking for an agent who represented people who's work I admired but also a list I thought I'd fit in with. My work is digital and my characters are stylized so an agent who gravitates towards traditional/realistic art wouldn't be a good fit for my portfolio.
I also took advantage of every skip-the-slush-pile submission opportunity I could. I eventually connected with Dan through PBParty, but also participated in a number of SCBWI and twitter pitch events.