Usually quite a personal thing but some general advice:
Build up to a technical shoe. I started with Scarpa Velocity for my first year and a bit, then went to La Sportiva Muiras as a more techy shoe and now use Scarpa Instincts.
Don’t go cheap (brands like Red Chili, etc.) because the shoes are crap.
Always try the shoe out. A lot of outdoor clothes places have a little wall to test them on. Most climbing centres will let you test them too.
Scarpa, Evolve and La Sportiva are the best brands IMHO.