Congrats in joining the world of showing. Hope your kitties like it too.
First of all 99% of cat shows also accept household pets for a separate class. There are a few on occasion (specialty shows) which would not have them - seen them in some CFA specialty shows. CFA used to have some very big classes, but they tend to promote the purebred and the HHP section is rather small. Good if you have a very nice cat to show as you will get lots of wins.
The other associations (ACFA, TICA) have large and competiitive HHP classes. These associations also treat the HHP's like purebreds with titles equilivant to Champion or Grand Champion
ACFA and TICA divide their classes into longhair and shorthair specialty and Allbreed (long/short together) classes for finals. CFA just puts them together in one group with one final for the judge.
As long as your kitties are spayed/neutered (over 8 months of age) you can show them - CFA bans any declawed cats. The others accept them but don't encourage the practice.
You want your kitty to be well groomed (especially a longhair), clean, and in good condition (weight proportion to size). Also pays to have a more mellow HHP since most come from only cat houses or one or two other cats and are not used to being in a room with 100 other cats!
I would try a one day show or about 4-5 rings total for the weekend to see if your cat likes it - shows are tiring for a first timer and you'll know in a few shows if you have a cat that really enjoys showing off and winning prizes. If your kitty doesn't like it, please leave him/her home and maybe try another kitty later.