good soldering technique and understanding what is going on when you solder: (a little wordy, somewhat dated and slow paced but the latter part of the video has lots of useful info).
I heartily agree a good quality temperature adjustable soldering iron is essential and it will make soldering easier, more consistent and you will get better joints. Something along the lines of the hakko fx888d (although the use interface is horrible) that has descent power and is reliable and has repeatable temperatures.
also good quality solder
and good quality flux
I would add a good quality multimeter, one that will not blow up in you hand if say by accident try to measure a 400V psu rail when the meter is in resistance mode... and yes I am speaking from experience here.... I was tired had already lecturer for 9 hours that day. its not cheap but I really like the brymen BM869s. - or one of the lower end models they seem to be very well made and robust. If the multimeter supports temperature probe(s) all the better for verify transistor case temperatures are not excessive etc.
joe smith one you tube has done some excellent videos comparing and torturing multimeters for reliability and high voltage tolerance.
for proper verification of stability, checking for clipping, etc a signal generator and scope are necessary. For a signal generator the bare minimum would be the analog output of a sound card on a pc and some software to generate sine waves, triangle and square.
given the high voltage outputs and rails the scope needs to have switchable x1 and x10 probes (x10 is actually divide by 10 so you can get 400V down to a more manageable 40V). Scopes can be dangerous to use since the ground wire on the probes is actually earth referenced and is clipped to something in the circuit which is not at earth potential you get the possibility of a short to ground....
Some form of desordering to 1. fix mistakes, 2 make repairs. The cheap option is solderwick or a spring loaded desoldering pump. The far more expensive option is a desloldering station. For me using a soldering iron and solder wick has resulted in to many lifted tracks and is too slow and clumsy. something like this works well and is worth its weight in 2sj79s. There are many similar types out there. it is temperature controlled and has a vacuum pump to suck out the solder.
For safety a variac is also very useful it allows you to slowly increase the voltage going into the psu so that if there is an issue it would hopefully manifest at lower voltages and hence reduce the collateral damage
once you get more serious a transistor tester and identifier can be very useful especially to check for bad components or to post mortem when the "magic smoke comes out". It can also do small signal transistor and led matching.
if you are going to do any surface mount soldering there are multiple ways to do it. fine tip soldering iron, hot air station, reflow oven. Magnification is useful - . The cheap ones can be really uncomfortable and can slide off your head easily but if your eyesight is not 20/20 I find them essential for surface mount and for generally inspecting joints etc.
now some "luxury" items to make life easier etc
The duoyi allows you to test high voltage zeners and also aids in detecting fake old stock transistors by providing non destructive transistor breakdown voltage testing. The instruction manual is crap and the sockets are junk. But with some modifications it works well.
another luxury is an LCR meter - this can allow you to match capacitors and inductors and also can measure lower capacitances e.g. a few PF than a multimeter can manage. It can also measure the effective series resistance of caps and other parameters so you can compare caps and identify worn out caps in old equipment.
super luxury items because you are addicted to building: distortion analyser
super luxury? ultrasonic cleaner. flux residue can result in joints degrading over time and at the voltages some stax amps work at e.g. the T2 the residue can conduct and cause failures.
super luxury: sometimes the provided gerbers are the wrong shape, don't fit your style and you wish you could change them. Sprint allows you to import gerbers, modify and re-export. Its relatively cheap.
https://www.electronic-software-shop.com/lng/en/electronic-software/sprint-layout-60.html?language=en
super luxury: sometimes you want to make your own schematics:
https://www.electronic-software-shop.com/lng/en/electronic-software/splan-70.html
super luxury: hands free thin probes for smd or when you don't have 3+ hands available. (The same company also sells hands free multimeter probes).
disclaimer, all items shown here I own personally and use regularly. However, other builders may have their own favourites and peoples priorities and build styles vary. So these are suggestions and nothing more.