In a word, yes!
Mine is of course from a Swiss source (that's where I live) but it works fine, all the way down 3 floors to my cellar workshop. It just plugs into our standard mains socket. You mount a door bell (push switch) on/beside the front door somewhere, then plug the main unit into a convenient mains socket somewhere.
Mine does need a battery for the front door bell push but I can't remember off hand - either a AAA cell or a silver zinc button cell - so you can tell how often I've had to change that battery can't you?
That's it, nothing more than the above.
As you say, there are "millions" of different models around. Mine was dirt cheap (20 quid-odd equivalent?) I forget, and I bet that apart from the fact that Swiss mains sockets are completely different to UK mains sockets, there's no real difference between what you've seen on Amazon and what I've got at home.
But you MAY have to be careful on max "radio range". As said, my house is on 3 floors (I live on the side of a slope) so the range of mine is more less vertically downwards, whereas you seem to be saying your shop is "down the garden" - i.e. further away from the main unit in a length ways fashion.
What difference (if any) that will make I dunno, but I guess when buying new (mine's yonks old, packaging long gone) your packaging will state max range.
HTH