First requirement for ALL HHP's is if they are over 8 months of age, they HAVE to be neutered/spayed. CFA shows ban any declawed cats (pedigree or mixed). ACFA and TICA allow them but don't promote it.
A good HHP will be friendly to strangers, like being handled by strangers, like to play with little toys (feathers, balls, etc that the judge may use).
They should be at proper weight for their size, well groomed (especially LH's) and clean, bright, shiny and a good personality. Ears clean, nails clipped and given a bath before the show.
The best way to find out is enter your cat in a local show and see how they handle things. By the 3rd or 4th ring, you will know if your cat is happy to be there or would rather stay home.
Ling went to one show - by the 3rd ring it was obvious she didn't like the other cats and was unhappy, so her show career was very short lived
I see you are in MN - there is an upcoming CFA show end of January. If you are interested in showing and entering, pm me - I'll give you the details and who to contact. Its a 6 ring show (I think) - 2 days - Saturday and Sunday. Its about $45-50 to enter one cat.
We will be showing Charlie there (altered class) so if you want to enter and bench with us, let me know - will be glad to help you out and give you pointers