Your choice of pedals will dictate the range of bike shoes available to you but there will still be a wide range of options available, and budget will dictate what kind of features you can pick from.
If you are going to cycling shoes ( as opposed to SPD cleats and MTB shoes for example), then the biggest decision is going to be whether to go for triathlon shoes or cycling shoes. The biggest difference is the fastening. Triathlon shoes are designed to get into and out of as fast as possible, which means they are likely to have a large opening and a single fastener. They will also have a loop at the heel which helps if you plan to do a flying mount.
Bike shoes are designed to hold you into the shoe more firmly, with multiple fastening points and firmer soles. They are designed for long rides so comfort and heat management are important.
The key difference is the speed at which you can get into an out of the shoe, so if you are planning on taking your time in transition, you are not likely to see much benefit from triathlon-specific shoes. However, if every second counts or you are planning to try flying starts on the bike, then triathlon shoes are a must.
Wiggle has a good selection here
What’s the flying mount and should I do one?
Bike shoes are specialised for being on the bike not off it, they are not ideal for running through transition! To get around this, triathletes developed the flying mount, where the shoes are fixed to the bike and the athlete runs to the mountain barefoot, jumps on and slides their feet into the shoes whilst moving and tightens their shoes on the go.
This is by far the fastest way to get through transition, but requires triathlon-specific shoes and a lot of practice!!
The shoes need to have a large opening so you can get your shoes on easily and loops at the back that allow you to tie the shoes to the bike with rubber bands which stops them catching on the ground. The rubber bands need to be thin so they snap once you start pedalling.
The fasteners need to be easy to tighten as you will be tightening whilst pedalling, and you also need to be comfortable on your bike if you want to try this.
You’ll hear a lot of talk about flying mounts/dismounts being one of the marks of a “proper” triathletes, but they will still be pretty uncommon at most races and can cause some pretty spectacular crashes if you get them wrong, so definitely don’t feel like they are required.