Mikefule

There is no limit to how many tools you can acquire over a lifetime in cycling and other activities. With a few exceptions which are absolutely bike specific (like a chain tool) they all have countless applications in other aspects of life. For example, a good set of metric combination spanners (ring at one end, open at the other), a good set of Pozidriv screwdrivers, and a good set of Allen keys. A 1/4" drive socket set is good for small stuff that you find on bikes. A 3/8" drive is a little more versatile for non-bike jobs, and a 1/2" drive is for bigger jobs like working on your car or motorbike.

Everyone needs a big, a medium and a small adjustable wrench (spanner) but should not use them by default. If you have a proper spanner available int he right size, use it.

Normal pliers, needle nose pliers, and good wire cutters (you can get specific ones for brake cable inners).

A chain whip in the right width for the sprocket. (1/8" or 3/32" for example.) One that is "too wide" will fit a narrower sprocket, of course. A chain whip is sometimes called a "freewheel turner" at least in adverts on Amazon.

If you have a freewheel, a compatible freewheel removal tool.

A C spanner for removing the lock ring. You will need the right size. A C spanner is sort of hook shaped with a tab at the end that engages with a notch in the lock ring.

A decent set of Allen keys.

In addition to a set of Allen keys for the workshop, something like this has many uses out on the road. They come with 3 sizes that you most commonly use.

A pedal wrench, if your pedals have flats where they screw in. Some only have Allen sockets on the blind side. A pedal wrench is a slim spanner of the right size to fit the flats.

A chain tool which can be used for splitting and re-joining chains, and freeing stiff links.

I'm in the UK and can find most of these things at Halfords, or local bike shops. They are also available easily on Amazon. One nice brand for bike tools, although slightly expensive, is Park Tool.