There are many good ways to save money in life. Purchasing climbing shoes online is not one of them. Climbing shoes need to be sized perfectly. One brand may fit very differently from another brand. The two biggest brands are 5.10 and La Sportiva. People tend to have either a "5.10 foot" or a "La Sportiva foot." For example, I only wear 5.10 shoes. La Sportivas simply do not fit my foot. The opposite is true for many people. I do wear La Sportiva Nepal boots for ice climbing, but boots are an entirely different story.
You might need a size 9.5 5.10 Anasazi, but a size 10.5 La Sportiva Mythos. The only way to know is by trying them on. Keep in mind that some shoes tend to stretch, and this should be factored into your decision. As a general rule, leather tends to stretch a lot more than synthetics.
Go to a climbing store and try on a great many shoes. Go to a real climbing shop, not REI. An employee should be able to recommend a good beginner shoe to fit your needs. There are of course super aggressive shoes with very downturned toes, meant for climbing the hardest routes. These will hurt you greatly if worn for any amount of time, and should be avoided at this stage in your climbing career. Background for informed opinion: I climb 100+ days of rock and ice each year, all outside, all over North America.