The main reason to build your own is to get a custom layout to your taste. Expense is a rather different matter, though you might just be able to do it on PC.
A knowledge of electronics I would argue is not really necessary as you can work around it easily enough, and a button is just a switch which is hardly the most complex thing. Indeed I would say fabricating a box and cutting the holes in wood or plastic for the buttons would be the harder part for the average person. If you buy the fancy illuminated switches then it gets a tiny bit harder but not a lot as it is only lightbulbs or leds and they tend to just want power of a certain voltage that is easy to generate, if not present by default.
Buttons will be the problem as not many places will sell arcade gear (there is some crossover between industrial buttons and arcade style stuff but it is not a normal switch or anything used by all electronics) so you kind of have to buy it online. Assuming your flag is accurate I am trying to think of anywhere I have been there with a lot of arcade machines (including things like mame cabinets), for if there are those there are people to repair said same and they might be a middleman for you/have some parts to sell. I don't know what the Dutch term would be but arcade buttons is the English one if you had not already guessed.
The PC is simple enough. You want something to act as the controller for it and for that something like the teensy++ will act as a USB HID (human input device aka mouse or keyboard) quite happily.
https://www.pjrc.com/teensy/usb_keyboard.html is part of the basic tutorial and covers how to turn a switch input into a keyboard. If you are looking at that and thinking you could do a rapid fire/auto fire quite easily then yes, yes you can.
If you are going to want to add a roller ball or analogue stick to the setup it gets marginally harder but you probably still can use something premade. As you seem to just want fighting games that is not an issue.
From the PS3 and 360 onwards third party controllers have been blocked and you need to buy the little lockout chips from Sony or Microsoft. They don't sell to just anybody though. However you can always buy a normal controller and cannibalise that, it is what all those "cheat" auto reload/auto fire controllers do. For PS4 controllers that is an expensive hobby, if you are lucky you will find one that is broken in such a way that you can still use it for this and it is going cheap. In my case I would realise that most people buying bad controllers probably want the plastic buttons, the shell and the battery rather than the PCB so there is that but you then might have to do some work. Equally I imagine many failures will be of the USB charge connector so you might have to first fix or work around that, not horrific to work around or fix but you will want someone that can solder for this one.
I have not got a premade listing of any test points for the PS4 but even if there are none (unlikely but whatever) it is all switches in the end so you just have to find where they go and solder to those.