Luthier Tools
Luthier? What the heck is that? It's just a fancy word for someone who makes guitars. I'm going to cover the absolutely essential tools, the very desirable tools, the tools that you'd like to have if you have a fairly large budget (and a spouse who will let you), and the stupid expensive tools that you might get if you have a lot of space and a very large budget. I'm also going to cover software tools that I use to do design work.
Essential Tools
You don't even want to try building a guitar
without a router. I use a Dewalt DWP611 router. These run
about $150 on Amazon but there are other much less expensive
routers available (just check the user ratings). Obviously,
you'll need some router bits to go along with it. The most
important being a set of top bearing, flush trim, 1/2" bits.
These come in sets of 4 with different lengths. You'll also
need a 3/8" bottom bearing, flush trim router bit and a 6mm or
1/4" router bit (depending on the size of the truss rod you
want to use).
You need a drill press of some sort. I've got a Wen 12" benchtop drill press and I love it but you can get by with a drill (which you need anyway) and a portable drill guide. Also, Vevor makes a highly rated 10" benchtop drill press for just over $130 (I suspect they're made in the same factory as the Wen drill presses). When I first started making guitars I used the absolute cheapest drill guide ever. Unfortunately, a drill guide won't allow you to use the StewMac Safe-T-Planer which is a tool that can save you a lot of work.
You need either a band saw (I use a Wen 10 inch benchtop band saw which is a bit pricey but you can use a smaller cheaper one) or a jig saw.
You need a random orbit sander. These are very inexpensive and most people already have one in their shop.
For making necks you'll need, at the least, a pair of diagonal cutters (but fret end cutters are better), a triangular file with the edges filed off (StewMac medium size is very good but expensive, look for LAMSAM on Amazon), a radius sanding block (there are some really inexpensive aluminum ones on Amazon), a straight fret leveling bar (reasonable on Amazon, or a very flat edged level), a fret end file (straight and angled, Metallor makes my favorite so far), and a fret slotting saw (.023 kerf from Solo Guitars or Edgetool on Amazon).
If you plan on doing any fine work, like inlays, you'll need a Dremel tool, a Dremel router base (the one from StewMac is excellent but it looks like China has caught up, you can get the Jiayouy Precision Rotary Tool Plunge Router Attachment on Amazon for less than half the price), Dremel down-cut spiral bits (I use 1/8” and 1/32” from StewMac but look around because those are expensive), and a rubber end or dead blow brass hammer (there are a couple of little kits on Amazon that have one of these along with a fret rocker and some other flotsam and jetsam).
Necks are, by far, harder to make than bodies but, even if you buy a pre-made, fretted neck (e.g. Guitar Fetish, Mighty Mite, Warmoth), you'll still need to be able to level, crown, and dress the frets. That means you'll need, at a minimum, the leveling bar and the triangular file.
There are a lot of tools needed to make a neck and they can get expensive but, if you're planning on making more than one neck, they're worth the money. A plain Jane maple neck with no nut, no markers, no side dots, and no finish will run you about $250 from Warmoth. As stated above, you'll still have to level, crown, and dress the frets.
In addition to the big tools you'll also need things like drill bits (metric and SAE brad point, normal, and SAE Forstner bits are useful), digital calipers (not absolutely needed but nice), glue (Titebond Original is my choice and, of course, CA glue), sandpaper, and clamps, clamps, clamps, and, did I mention, clamps. There is no such thing as too many clamps.
Desirable Tools
An oscillating spindle sander can save you a ton of time. I've got the Wen 6510T and it works great. When it dies though I will be getting the Wen 6524 oscillating belt and spindle sander. Two birds with one, slightly more expensive, stone.If you don't have a 13" or wider thickness planer then the Saf-T-Planer from StewMac is the next best thing. I used one of these for years.
You can slot the nut with a piece of the correct gauge string wrapped in sandpaper but you probably don't want to. There are also some little round nut slotting files that come with some of the cheap luthier tool kits on Amazon but I've never tried them. I've been using a set of Nomad nut files (for 10s) and they work fine for 9s. You can rock them to get larger slots. Yeah, they're pricey.
A fret slotting jig (I like Solo’s, you also need one or more templates to go with it). You can make your own fret slotting jig from plywood and it works just as well, it just takes longer. I did my first six guitars that way.
Robo-Sanders from Klingspor are really handy. These are just drum sanding drill bits with a guide bearing (you can get by with just the 2"x2" ). Of course, these aren't absolutely necessary either.
A fret tang nipper from StewMac can be used to recess the tang at the end of the fret so you don't have to look at the metal at the end of the fret slot (this isn't really necessary, I just think it looks better).
A scroll saw is very handy for cutting out MDF templates and some small pieces (although a jig saw will work just as well and then you clean it up with sandpaper).
A laser engraver is super useful but definitely a luxury. I've got a Sculpfun S10 laser with a blower and a Y-axis extension. The price on the S10 laser has dropped like crazy lately. At this time it's on sale for $269 (with the blower). I spent quite a bit more for mine. One thing to keep in mind is that a diode laser like the S10 will not cut through anything reflective and it's fairly weak so forget about trying to cut pearl or abalone with one of these. However, you can make some amazing wood marquetry inlays with it and, if you have the Y extension and the air assist blower, you can use it to half cut through MDF for templates (cut half way through, use a jig saw to cut out the edges near the line, pop off the remaining MDF where it was cut through with the laser, then flip it over and use a 3/8" bottom bearing flush trim router bit to clean up the edges). One of the biggest problems I faced with the S10 was what settings to use for each type and thickness of wood. To that end, I started keeping a file with a list of what LightBurn settings worked best for me. Of course, every piece of wood is different so these are just starting guidelines. Test on a scrap piece before you start burning. In addition to cutting marquetry inlays, recessing for said inlays, cutting templates, and drawing templates for pickguards, I also use the S10 to make wood pickup mounting rings and knobs. I'll describe that at some point in the future.
Stupid Expensive Tools
I finally bit the bullet and bought a Wen PL1337, 13", two-speed, spiral blade, thickness planer. Is it absolutely necessary? No, but, holy cow, the amount of work it saves you is amazing. It planes so smoothly that you almost don't need to sand. I only use it on slow speed and set the cuts at about 1/64". This makes it much less likely to have tear-out issues.CNC router? Forget it! If you get one that is large enough to handle a guitar body and/or neck you're looking at well north of $1000. Not only that, you need a lot of space and some form of vacuum waste setup. They are also very slow. If you're going to do carved top guitars one might be useful but it's just about as easy and, arguably, faster to do that by hand with a router. It would just require more cleanup during and after routing. If you're doing flat bodies with some form of beveling or curving on the edges it's way faster to do it by hand. One of these might be nice for making necks but it doesn't take all that long to make a very good neck by hand.
Software Tools
GIMP! The GNU Image Manipulation Program. A cross-platform image editor. What's not to like? It will do almost everything that PhotoShop will do and it's free. I use this to design all of my templates, inlays, f-holes, pickup mounting rings, etc.If you have a laser, LightBurn is the best available. It ain't free though. It also doesn't work on Linux (although it used to so I can still use my old version). I am, at present, playing around with RayForge to see if I can dump LightBurn.