Aside from some solder and some resin to help it flow, these are the items that have been most helpful to me. Total cost of all items is around $40 US, so not expensive. You can certainly spend more and get better stuff, but I have used these items for pretty much everything I have soldered except plumbing fixtures ;-)
First item is a cheap soldering station that. Nice to have one that is adjustable from 20-50w. Second item is a cheap 3rd hand. I actually have two, and often use both. A cheap set of "precision" pliers. My set was about $7. Precision does not mean expensive it just means small. A magnifying visor. I tell myself this is not because of my aging eyesight. It's because some of this stuff is small.
I forgot at least one other thing that should be part of your kit...
...a wire stripping tool. You can do pretty much any soldering a guitar requires with these few items.