You don't really need any special tools, any more than you need a string winder. They can make things easier, but they are not required.
It's only been the last 4 or 5 years that I've actually bought specialty tools. All you really need is your eyes, ears, a capo, and if you'd like, a set of feeler gauges from the auto parts store, and that's all I used for 40 years.
Step 1 - Capo the 1st fret and hold the strings down at the last fret, holding in playing position.
Pluck the string between the capo and your finger... does a note ring clearly? If not, the neck may be too straight. If it does, can you barely slip a business card between the string and 7th fret? That's about right.
If not, adjust the truss rod to obtain that condition. Tighten to straighten the neck and reduce clearance, loosen to open up clearance. Give the neck a little time to settle in and re-check step-1 as needed.
For fun, "play" the neck backwards and see if you get a clear note all the way to the top (with the capo still in place). This can reveal high frets without a fret rocker.
Step 2 - Lower your saddles until the strings start to buzz, then bring them back up until the buzzing clears. Adjust the saddles to a smooth curve that has all of the strings about the same height above the neck. "Book value" is 4/64"... but some prefer higher, some prefer lower, some guitars won't go lower. If you play with a lot of bends, you'll need to go a little higher or you'll fret out on bends.
Step 3 -Adjust pickup height. Book value is ~ 1/8" down from the strings... Strats tend to "like" a little more on the bass side. Too close and it can cause problems with intonation.
Step 4 - Intonation. A strobe tuner is very helpful, but not needed. Got $10 and an Android/iPhone? Peterson tuners has a strobe tuner app that uses the phone's mic.
So for intonation, tune to pitch, check the 12th fret harmonic (should also be in tune), and fret the 12th fret. If the note is sharp, tighten the screw to pull the saddle back away from the nut. If the note is flat, loosen the screw to move the saddle closer to the nut.
Repeat until the open string and 12th fret are both at pitch. Repeat for the remaining 5 strings.
Intonation is always the last step, because steps 1-3 will impact intonation. Likewise, the truss rod adjustment will impact string height.
There ya' go
Unless the neck needs to be shimmed, or there is a problem with the nut height, you've just completed a basic setup with nothing that you can't find in virtually any home.
The Stew-Mac radius gauges are the biggest ripoff on the planet. For one, you can't change the string radius with a Gibson style bridge. Just adjust all of the strings so they are the same height above the neck, and that will establish the radius properly.
Here's a couple of screenshots from the Peterson app with a 440 tone played on my PC...
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Click to expand...