There isn't really a correct amount of shoes you should have. Some people have just one pair, while others may have many. More experienced climbers tend to have at least a couple of shoes, and professional climbers usually have quite a few shoes.
The amount of shoes you should have does not necessarily depend on your climbing experience. Professional climbers have many shoes because they actually need them. They go through their shoes quite quickly due to all of their training and competitions. Climbers who are not professional climbers, but are more advanced, sometimes end up having a few shoes because they just bought them with time.
If you are just starting out, just having one pair could be more than enough. Some like to have a pair that is used only for warm-ups, and another that is used for their harder climbing and projecting. Some climbers also like to have 2 pairs of climbing shoes so that if one pair is being resoled, they can still climb with the other pair.
Some buy shoes because they are on discount also.
In the end, it depends on your needs, and budget of course. There is no general correct amount of climbing shoes a climber should have.
It depends on your goals, the purpose of the shoes, and on your feet. If the shoes are meant to be more of a performance fit, then they should not be too big or loose. If they are meant to be a comfort fit, or shoes for warming up and for easier routes, then they can be slightly bigger if you feel it's necessary.
All of my climbing shoes are half a size bigger than my street shoe size, and this is a performance fit for me. I have flat and wide feet, and have found that going up half a size is the perfect fit for me. It's not loose, but it also isn't painful.
Also consider that if you are buying leather shoes, they will most likely stretch by half a size up to 2 sizes, so if they are half a size bigger when you buy them, they may very soon end up being over a size bigger, or more. So the type of shoe you are wearing also matters when answering this question.
Whether wearing climbing shoes that are too big, or bigger than the actual size you need, is ok, depends on your goals and the reason why you are wearing shoes that are bigger than you need.
Many climbers have shoes that are specifically for warming up on easier routes. This allows them to get their feet a little bit warmed up and ease into wearing the smaller and tighter climbing shoes. It also allows them to climb more comfortably without the feeling of pain or discomfort that comes with smaller climbing shoes.
For warm up routes, it's normally ok to wear bigger shoes, as you probably will not need the precision and performance of the smaller and tighter shoes. If you are planning on wearing bigger shoes for harder routes, or for projecting routes, you may have a hard time as the bigger and looser shoes can reduce your performance, especially if you are working on hard routes with small foot holds that require a lot of precision and the ability to apply a lot of force to your toes or heel.
In the end, it really comes down to experimentation. Experiment with different shoes and different sizes, match them to your goals and purposes, and find what works best for you.
It can take anywhere from a few sessions to a few weeks to break in climbing shoes. The amount of time it takes also depends on the fit and stiffness of the shoes. Some climbing shoes may be more comfortable from the beginning and require less breaking in than others.
Many climbers choose to climb just a few routes each session in new climbing shoes, and to gradually increase the amount of time spent in them. This will extend the time it takes to break in the shoes, but, if the shoes are unbearable to wear, it may be a good option.