Always buy the best tools that you can afford. Not only do they last longer, but they also don't damage your guitar. As an example of this, cheap screwdrivers are badly made at the tip and can chew up screwheads, making adjustment or removal well-nigh impossible.
Here's a collection of tools that I have acquired over the years. I haven't described or shown you the whole lot, just those which will make up a basic set-up kit.
You need a range of these but, as a rough guide, you'll need a large and a small one for slot screwheads and the same for crosshead screws. You can get sets of tips with a handle, but you don't want to be replacing tips all the time, so my advice is to use separate screwdrivers. You need screwdrivers for very obvious reasons - undoing screws - but a less-obvious use, until you come to do it - is adjusting a trussrod which has the screw at the body end of the neck. You also need screwdrivers for pick-up height adjustment and for setting the pole-piece heights. Trem adjustment is also impossible without them.
2. Allen or Hex keys.
You may be lucky and get these with your guitar, in which case, keep them with the guitar and look after them carefully. Hex keys are easy to obtain and generally cheap.
I've put handles on a couple of mine. It makes them easier to use and more comfortable. The small one is for the bridge screws of my Tele and Strat and the larger one for adjusting my Strat's trussrod. Hex keys are also necessary to adjust locking-type trem units.
3. Wire Cutters.
Guitar strings are made of very hard steel and you need good quality cutters to cope with them. Cheap cutters just get nicks in the blades and are useless almost as soon as you start using them. There are a couple of types I use. The side cutters do for all sorts of jobs, but the others are good for accessibility around the head of the guitar.
4. Steel Rule.
When it comes to this item, you need to find one that is graduated to sixty-fourths of an inch. Not easy to find, but not impossible. You need this to set action and pick-up height amongst other things.
5. Feeler gauge
You'll need this to measure the action. A set of both imperial and metric are handy. I think these are sometimes called spark plug gauges
6. Socket Wrench.
Sometimes, as with my Les Paul, the trussrod adjustment is made with a socket. Because of the access you need a socket attached to a screwdriver handle. It also helps if the socket is a "long throw" or deep type.
7. Nut Tools.
Needle files are good for cutting the nut slots for the wound strings, whilst a piece of junior hacksaw blade with the set knocked out will cut slots for the plain strings.
8. String Winder.
An invaluable tool! saves hours of winding and also has a bridge pin puller for acoustic guitars. Buy one. Don't put it off. Buy one now!
9. Bridge Radius Gauge.
As long as you know the radius of the fingerboard of your guitar, you can make your own. You will have to compensate for the fact that the wound strings have to be set slightly higher at the bridge. You need this for Fender bridges where each string saddle can be adjusted individually. Gibson saddle heights are preset. With Fenders you have to "mirror" the fretboard radius in the saddle heights.
10. Neck Block.
This keeps the guitar head off the flat surface you're using to work on and also makes working at that end a lot easier. I made mine out of a couple of bits of scrap pine I had left when I put a new door on my bathroom. I then padded it with foam to protect the guitar neck.
You also need a piece of carpet to lay on your work surface to protect the back of the body and some means of tuning the guitar to pitch. This could be an electronic tuner, pitch pipes or a tuning fork. I use an electronic tuner myself. A capo will also be needed when you come to adjust the trussrod.
A good purchase is a small tool box in which to store the various tools. some are quite small and easily lost.
Of course, you may have many of these tools already and only need to buy a few to make up your set-up kit.