But I've never bred a cat before.
Don't do it. You are not a breeder, you will not be breeding her to better the breed, and that is all a cat should ever be bred for... otherwise you're adding to the 50+ million cats that live on the street in America, and millions euthanaised yearly in shelters. Even if yours find a home, you displace others that may have been able to find a home otherwise.
I'm reading about it online and it seems like a pretty hefty/costly endeavour.
It is. To breed properly you do not make money.
I realize I should consult my vet and make sure she has a physical check-up before the mating starts. I'm actually planning on taking her to the vet tomorrow or the next day. But is there other things I should know?
Not just a physical check-up, you must do DNA testing on all known genetic conditions that could befall the breed and make sure before EACH breeding she had not developed those issues. You also cannot breed her until she's around a year and half to allow her to be fully grown. They only breed about once a year (and put up with the awful yowling the rest of the time) and spay after a few years. Otherwise cats become babies machines. Most breeders also show their cats, which is crucial to knowing if you have a breed standard cat and where it ranks, they also must breed for temperament. They also must be prepared to pay for 1,000+ dollar c-sections, the loss of their cat in pregnancy, or kittens with birth defects that may need to stay with you for life. A good breeder also takes back cats they have bred at any time of their life; they brought them into the world, they are responsible for them.
A lot of the things I read on the internet keeps telling me I should be spaying her, even after she's had a few litters. Is that true? Do I HAVE to spay her at some point?
YES. To spay before the first heat cuts down on mammary cancer by around 95% or more. A cat gets spayed not just to prevent the needless kittens they will no doubt have, sometimes they will even have kittens on top of kittens -- before the last are weaned. Cats go into heat FREQUENTLY. When they do they are loud and try everything to escape the house. They make better house cats... you cannot live with a cat in heat, they are nuts. It is not fun for them either.
Are you aware the keeping an intact MALE cat is disastrous? Most breeders keep them segregated in their home from other cats. They spay, especially when they small a female in heat -- which they will smell if the cat is in the same house. Cat pee destroys a home... and smells awful in the process. After neutering a male that's started spraying, that does not always cure the habit of spraying.