Question: Edit: everyone who's answered has been very helpful -- I tried to select all 3 answers as "the" answer but in the end it only let me choose one. Thanks to all!

I'm interested in purchasing my first pair of clipless bike shoes, principally in order to get the bike fitted properly, but also for performance reasons. I've put it off until now because I've been a bit nervous about getting stuck and falling over.

I'd welcome your recommendations on what to look for, how they should fit (in comparison to regular shoes, as well), whether there are any types or brands that are 'safer' (easier to unfasten from the pedals in an emergency), and whether there are any tips you can offer from your experience.

For what it's worth, I have a Giant gravel bike which I'm riding solely in asphalt at the moment, but am thinking of moving to a road bike one of these days.

Thanks in advance

Answer: 
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.

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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.

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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.
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> I'm interested in purchasing my first pair of clipless bike shoes, principally in order to get the bike fitted properly, but also for performance reasons. I've put it off until now because I've been a bit nervous about getting stuck and falling over.
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Don't be nervous. You'll learn the unclipping motion instantly. I have never crashed due to not being able to unclip quickly enough. Actually what is hard with clipless pedals is clipping in, sometimes it takes a second or two. But unclipping is easy.

The most important feature you want to look for is that you must be able to walk on the clipless shoes like you walk on regular shoes. An unfortunately large fraction of clipless pedal systems has protruding cleats that prevent walking. So you can't stop and buy something to drink at a grocery store ... unless you like to walk like a duck.

Fortunately, Shimano sells SPD pedals (regular SPD, not SPD-SL) that has the cleats embedded in the shoe in a manner that allows walking on the shoes.

With SPD, you can select single release and multi release cleats. Single release cleats allow unclipping only for the intended unclipping motion. With multi release cleats, you can basically unclip using any motion. I recommend single release cleats. It's not that hard to learn the unclipping motion. With multi release cleats, there's the problem that regular forceful pedaling can cause an unintended unclipping event, causing you to crash.

The Shimano SPD pedals have a tension adjustment screw so you can set the tension really loose for training clipless pedal use but you'll want to tighten it later when you have learned how to clip in and unclip.

My recommendation for the pedals is PD-T8000 because they have the mandatory pedal reflectors required by the law in many jurisdictions, and they also have a regular side that allows you to ride on any shoes, not just clipless shoes. You might think having clipless side on one side only would be bad because you never know which side is up, but these PD-T8000 pedals have a heavy side and a light side so when stopping they are in a well-determined position. So this allows you to time putting your feet on the pedals in such a manner that you always repeatedly hit the side you want to hit.

You can select shoes from Shimano or from some other brand, but do ensure they have the two-bolt attachment for SPD cleats. At least Shimano shoes are sized such that a given size is sold with a bit larger number so the usual advice is to select one size up. For example, my regular shoes are size 43 but I use size 44 Shimano shoes.

Also if you ride at 5 degrees Celsius or colder, you'll want to buy a separate pair of shoes that are intended for cold weather, and if you ride at arctic temperatures you'll need a third pair of shoes for extreme cold.