Bike peeps
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Correct, as far as I know. SPD cleats allow you to clip in, but the clips are recessed so you can walk without looking like a fucking duck. For my indoor cycle I have shimano SPD cleats like this, but I see there are some cool options out there like this if you are out and about, too: https://www.adidas.com/us/adidas-five-ten-trailcross-pro-clip-in-mountain-bike-shoes/HP9935.html
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Road shoes are far and away easier than SPDs to detach and reattach. But they aren't recessed and the duckwalk makes you look like an asshole.
There are no ideals, only compromises.
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What you want are "MTB cleats". SPD is one example of them, but there are more, e.g. from Time and Crankbrother.
I have both SPD and SPD-SL shoes (the latter being the road style version). With SPD shoes you can more or less walk normally and don't look like an idiot. With SPD-SL you don't want to walk for more than 10 metres.
Some people will argue that proper road bike cleats have advantages, such as more efficient transmission of power or more comfort on the bike or easer click/unclick, but to be honest I couldn't tell the difference. If anything, the MTB cleats are easier to lock/unlock, especially when dirt is involved.
Unless you are a pro, the main argument in favor of "proper" road bike cleats is that you will wear what all the others are wearing in a group ride.
The pedals you need depend on the system you are using, but I guess you know that already.
Don't buy Wahoo pedals. I tried them once. They are very expensive but real shitty.
