Depends on what you call "tinkering".
As
@Sharky has said, for basic maintenance all you need is a multi tool with allen keys, and maybe a chain splitter. Want to remove the cassette? Get a chain whip (to stop cassette spinning while you try to loosen it) and the appropriate tool for loosening the lock ring, depending on what type of cassette is fitted. Want to remove the bottom bracket? Depending on type of cranks you might need crank pullers, and again there are different types and sizes. Plus you'll need the right size of bottom bracket tool.
Other useful tools are tyre levers, spoke key, pedal spanner, cone spanners for removing your wheel hub bearings, bearing presses if you're planning to replace your headset. Cable cutters too.
So all in all, it's not quite as simple as just buying a "tool kit", as it depends very much what you intend to do, and what type of components are fitted to your bike.
Edit to add... Don't be tempted to buy some of the cheaper tool kits on the market. They are cheap for a reason. Chain splitter tools in particular, you need a decent quality one, or you'll be throwing it in the bin. Same applies to cable cutters.