If you're going indoors and you haven't climbed before I'd suggest renting for your first few sessions, as shoes can be expensive and you might find bouldering isn't for you.
Most climbing/bouldering gyms I've been to have rental shoes that will be vastly superior to climbing in your regular trainers.
If you get the bug, have climbed before or are going outdoors the honest answer is whatever fits your foot.
You'll find a lot of people online recommend going down a shoes size or even several when buying rock shoes. For your first pair I'd disregard this advice. Go with something that's snug but comfortable. Also for a beginner shoe I'd recommend you stay away from anything too aggressively downturned as these will play havoc with your toes.
You're going to be looking for something that fits your foot with the least amount of dead space inside possible, so try on as many as you can to find the brand/model that suits you before buying.
As a point of reference I started with Evolv Defys as they were cheap(ish), relatively flat and seemed to fit quite well. Other potentials could be: Red Chili Durango, La Sportiva Tarantula, Scarpa Velocity etc.
Whatever you buy/rent have fun!