My z-axis travel speed is too fast in my opinion, but x and y axis travel speed too slow. But if I just change the "travel speed" variable in the slicer, all three speeds will be affected. Is that normal?
Yes it is normal. All of your actual max speeds should be set in the firmware to prevent trying to move too fast.
The most important to set the max in the firmware is the E max speed. This will allow you to set the retraction speed in the slicer to something like 500 or 1000 and then let the firmware limit it. By doing this you can change the print speed via an LCD or host while printing and not have it effect the retraction speed. So lets say you set the max E speed to 300mm/s in the firmware and 30mm/s in the slicer. Then you turn the speed down to 5% via the LCD because the top of the part being printed is just two skinny posts that need to be printed slower. This would cause the retractions to take place at 1.5mm/s which is to slow and will cause more ooze than not retracting at all. But if you have the limit set in the firmware to 30mm/s and the slicer is set to 1000 and you slow it down to 5% you will still be retracting at your max retraction speed of 30mm/s. You can actually do the same thing for travel speed and Z speed if so inclined.