Check out this webpage: http://slagcoin.com/joystick/attributes_brands.html
There is a data table for joysticks a little over a quarter of the way down.
"Plate To Base is the distance from the top of the mounting plate to the bottom of the joystick (ie the bottom of the shaft)"
Also note the S-Plate column if that applies to you.
Remember to add and subtract the appropriate values as needed for the thickness of your control panel itself, depending on whether or not the stick is top-mounted, bottom-mounted, and laid flat or recessed or whatever.
There is also a data table for pushbuttons a little over a three quarters of the way down.
"Depth is the distance from the bottom of the rim (ie the top of the panel) to the bottom of the button; note that Sanwa and Seimitsu switches can be bent to trim the depth up to 7mm"
Basically, this number minus the total thickness of your control panel gives how far underneath the buttons will stick down.
Depending on your your arcade stick is assembled, remember that you may also need to take into account the thickess of the actual top and/or bottom as well.
For what it’s worth, as long as the empty space inside the case is deep enough for all your parts, it should already be more than deep enough for pretty well any boards or wiring you do in there.
Hope that helps.