Just to correct the first reply in this thread, Rabies and Distemper are NOT, I repeat NOT airborne. And for perspective, according to the NYC dept of health the last cast of human rabies in NYC was over 50 years ago.
In our shelter, (in NYC) and in other shelters in the NYC area I believe without question the number one transmittable illness (that can vector from cat to human to cat) is viral upper respiratory illnesses (basically colds, or worse, Calici [FCV]). Cats are vaccinated for Calici when they get the 3 in 1 vaccine (FVRCP) but that won't always prevent infection but will usually lessen the symptoms significantly. Cold viruses are very hardy and can easily survive on your clothing and body.
Ringworm as widely discussed above can be transmitted to your cats and to you, and while very hardy in the environment isn't hugely contagious. Diluted bleach (10% solution) is one of the few things that will kill it, but make sure your cat never comes into contact with bleach. Anti-fungal creams that contain 2% micanizole nitrate are a good and safe treatment for ringworm, both for you and for your cat.
Your cats are only at risk of Distemper if they are unvaccinated.
Hopefully your organization requires you to use different latex gloves for each cage you clean or work with, and if they don't I'd suggest you use them anyway, changing gloves between each cage.
Everyone has their own routine for not bringing home illnesses, based on their own experience, level of concern, and depth of contact with the cats. The work I do at our organization allows me to have only minimal direct contact with our cats, and because of that i only do the following:
- I remove my shoes before entering my home.
- Once inside I go directly to the bathroom without touching my cats and:
- Rinse off the soles of my shoes.
- Remove my shirt and put it in the hamper.
- Scrub my hands and arms well with hot water and soap.
- Sometimes wash my face depending on cat contact prior to coming home.
When I had more contact with the cats I brought a 2nd shirt to the shelter and changed there, and then bagged the shirt, and would immediately shower once home and put all the clothes in the hamper, often in a plastic bag.