For many other things in life, I tend to buy first and learn how to use later. For bicycling, I've tended to discover the need, then buy the tool.

I started with the typical 4mm/5mm/6mm triangular allen key. Versatile, though hard on wrists and doesn't always fit. Next was an allen wrench kit - I think I have the Pedro's kit, where the long side of each allen wrench is a ball head, so it's easier to move the wrench around when starting the screw. A set of screwdrivers (that's theoretically only to be used on the bike) came next, and has been very handy (even if I have borrowed from this kit and not returned some, naughty me).

I do throw too much money at my hobbies, and for a tool box that's true. I went with the Park PRS-15 repair stand (discontinued, I believe). I added the BTK-1 tool bucket with "kilt". It's a skirt that "attaches" to the bucket, with lots of pockets for tools. Every tool has a home, and it comes with a paper towel holder that fits the other side of the stand. On the rare occasion that I take my tools with me, the kilt comes off the bucket and fits inside the bucket, so my tools don't go flying and hiding.

I've since added a 15mm pedal wrench, chain whip, freewheel "bit", bottom bracket "bit", 1" wrench (for the two bits), and a Torx tool to deal with the screws on my disc brake rotors. I suspect a chain tool is in my future.