Your first pair of climbing shoes should be comfortable, durable, and versatile across disciplines. New climbers move between bouldering and top rope frequently — sometimes in the same session — so you want a shoe that performs in both contexts. Aggressive performance shoes are not the right call for first-time buyers; they hurt, they wear out fast, and the performance benefits do not show up until V4/6B+ anyway.
The shoes below all share a flat or near-flat last, comfortable break-in period, and reliable rubber. Any of them will take you from your first session through your first year without fighting your foot.