I disagree that you should wait until some magic moment when they're ready - it used to be common to potty train at 18 months or 2, or even younger, when not being potty trained involved terry nappies. Basically modern nappies are so cheap and convenient that people put it off longer but it is possible earlier.
We used the oh crap book, you start with a potty and bare bum in the house and sit them on whenever they start weeing, once they get themselves to the potty then you let them wear loose trousers and still help them on, when they've got the hang of that you add pants, then you start going out for short journeys.
I found potty training surprisingly emotional, it's the first time you are handing over responsibility for managing a body function to your child and it's an important step towards independence.
You will need to get over your thing about public loos. Being overly clean is also bad for kids' immune systems and linked to allergies, we're not meant to grow up in sterile environments.
If you're going to find it hard to deal with leaks and spills then I'd leave it a bit later, there's a fair bit of mopping up in the early days!
Potties only last until they're a certain size, then loo seats are better but they need to be able to get there in time, and if you only have one loo in your house then a potty is a useful back up as they might not be able to wait until the other person finishes.