You need shoes, cleats and pedals all to be compatible.
(There's also an implication that you have two feet, and nothing unusual there.)
Shoes have to fit your feet comfortably, with a close fit around the rear and across the instep. Personally I find a slight roominess around the toes to be ideal. You can get shoes with laces, velcro, ratchets, elastic and weird string systems, none of which makes a big difference.
The shoe has to fit the cleat, and there are two main interfaces being 2 bolt and 3 bolt. Some shoes have 5 holes to fit both styles, but they're relatively uncommon. 2 bolt shoes often recess the cleat into the sole a bit, so that walking is mostly normal, whereas 3 bolt cleats are totally below the sole and walking in the shoes is unpleasant, and only for short distances.
The pedal you choose has to match the cleat - most new pedals come with a starter pair of cleats in the box.
3 bolt cleats tend to be made of plastic and are good for 3-12 months of usage, depending on how much you walk and how often you put your foot down. I found my left foot wore twice as fast, mostly due to my habit of rotating onto the bike.
2 bolt cleats tend to be made of metal, and they last much longer. However the walkable shoes tend to be softer and less "efficient" at transferring power. So fast roadies still go for the cloppy 3 bolt road cleat. 2 bolt cleats are reputed to cope better with mud, so are more the domain of the MTB and the cyclocross runner.
You can ride a road clipless pedal while wearing flat shoes, provided the sole is stout. There's less platform so its a lot more slippery, but it can be done. You can also slip some old cleats into the pedal to make it better, or purchase some "platform adapters" in case you want to ride the road bike to work/shops but wear normal shoes.
It is totally okay to ride road 3 bolt pedals on a MTB, or 2 bolt pedals on a road bike. Noone changes their shoes between the different sorts of cleats regularly, instead they'd buy two pairs of shoes and leave them set up. Given pedals are cheaper than shoes, it is acceptable to have several bikes with the same style of pedal.
I got some clipless shoes ~5 years ago, and I have never fallen due to the shoes. That you have to fall a couple times is a myth. While it might happen from a moment of inattention, just learn to unclip while coasting up to a stop and you're generally fine.
I've had minor slips (not a fall) when walking in cleats, and sometimes while stopping because the cleat didn't give great traction on the road surface especially when wet.