Whether you're bouldering or being belayed, you're going to need climbing shoes, and the first few times I went, I just rented. But at $5 a day, that adds up! If you're ready to commit, invest in a pair of climbing shoes to save you money in the long run.
Beginners should go for a neutral sole, which means it's fairly flat and more comfortable than the soles that are moderate (slightly curved) or aggressive (very curved). I got a pair of these Black Diamond Momentum Vegan Climbing Shoes ($95). Climbing shoes run small so you'll probably want a size or size and a half larger than you normally wear. I'm a 7.5/8 in regular shoes and I got these in a size 9.
Note that you want to wear your climbing shoes without socks (another reason to buy your own), and you want them to fit very snug so your feet have more control. They'll stretch out a little with time, so you might want to buy a shoe that feels a little too tight. Many climbers only wear them when they're actually climbing because they're so uncomfortably tight, and they'll take them off in between climbs.
