Anyone on here go climbing?

More echo for the above general information. If you're just sort of staring to climb, get what fits and is comfortable.
start at your shoe size and work down if you feel like your foot is slopping about inside them. Your foot wants to be held firmly but you still want to be able to walk about and not have the toes curled too tightly together.

The whole 'buy a size smaller thing' doesn't always work and stubbing your toe in shoes that are too tight will finish your day in my experience.

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It will be a little uncomfortable but should not be unbearably so.

Same as most things, there are specific shoes for different types of climbing. I'd disagree with the idea of trying on all the shoes in the shop. Just ask the person there what they would suggest for the type and level of climbing that you're doing.

Personally, I'd avoid shoes which are canvas lined. Yes they may be more comfortable initially but they tend to smell after a while. They tend not to stretch much if any.
Unlined shoes will stretch more (and smell less).