Personally you can't go wrong with Shimano. Your bike is Shimano 105 so it stays in the family. Basically there are two types of pedals SPD and SPD-SL. The first are more for mountain biking, commuting and general cycling. This is because the cleat is recessed into the shoe that allows you to walk comfortably. They use two a two bolt design to hold the cleat.

The second type is SPD-SL which typically has a stiffer sole and an external cleat that makes walking difficult. The benefits are a bigger contact area on the pedal and they are generally stiffer and more efficient. Here I recommend Ultegra SPD-SL. Inexpensive but works well. This type of shoe and cleat use a three bolt design.

Next there are others Egg Beaters, Speedplay, Look and others. There are benefits to these pedals and each one is unique.

Purchase shoes to match the pedals, three hole vs two hole.

Again I do recommend Shimano because they are the number one pedal sold, you can find cleats anywhere and generally just good.