You're using steppers? Nema 34, low mH inductance values, good quality drivers, either gecko, or leadshine. 2:1 or 3:1 belt driven gear reduction for X and Y spring loaded into the pinion. You can either use a commercially available carriage or make your own.
For the Z, 10mm lead ballscrew, depending on spindle weight and if you want to counterbalance it pneumatically. 5mm would also work, but not as fast. If you buy a premade linear stage from EBay or somewhere else to use as a Z axis, then a leadscrew is fine. Just be careful, you want 2 bearing blocks and two supported rails per side. The cost of a 16mm or 20mm ballscrew isn't very expensive so if you make your own Z axis, do that. Unless you already have free parts somewhere. It's not critical.
I do performance calculations with graphs and including inertia sometimes. This is a pretty straight forward build if I understand it correctly. What you are talking about is like one of the many CNC Router Parts builds, or Fineline Automation Saturns. If you were using servos with different gearing and heavy weights, and some very specific performance targets in mind, then yes, it's worth it to calculate.
Why 750? Did you not mention you want to cut sheet products? Like plywood? I assume those are travels because it looks like you want to cut an 8' x 4' sheet with this?
Yes on being able to disassemble. I am doing that on my build. only way to move it in and out of a basement. No on the 50 x 50 x 3 box. It's too small, and will distort too easily when welded. Try to get some larger sections. Way easier. Even go to your local steel scrapyard and see what they have.
How you incorportate the 4th axis will need to be well thought out from the start.
Nope. Make up your mind now if you want to design a 3 axis or a 5 axis machine. Was this the reason for the 750mm? You would really need to design the entire machine at the start. 5 axis machines are hard to do and expensive. That is why they are rare. You mentioned cost twice in your post. Perhaps this isn't for you.
If you want some better feedback, then you will need to draw up what you want to do in CAD and post some pictures of your designs. That's the best way to get relevant help when designing.
Yes and no. It depends on alot. You usually have to get the steel flat either by machining or using epoxy leveling, so there is some time and money expense there to consider. Aluminum typically comes flat enough already.
So you want to build a machine that you can make longer in the future? How do you wish to accomplish this? And by how, I mean, please post some pictures of your design, drawn in CAD, showing how. I don't see this working out.
You will end up upgrading the entire machine so there are three original bolts left and a piece of steel tube by the time you're done upgrades and you haven't even built the original yet.
So you want a 3 axes machine that will has a cutting area of 2600mm x 1500mm with a rotary axis.
That you can easily convert to a 5 axis machine keeping the additional rotary axis.
That you can easily upgrade the spindle to a larger one.
That you can add an addition on for longer movement later.
That you can also use as a CNC plasma machine.
Did you mention a budget? LOL! Let me guess. Is it $2000 to $3000 USD? Am I a mind reader?
With a gantry weight of 75 kg. No, this is too light for a 5 axis with a long movement. Your Z axis assembly will weigh twice as much as your gantry!
You forgot 3d printer. Just saying.
At this point, it's not looking very good. You will not meet all of those expectations. I'm being kind with the way I worded this.
Buy a kit or use plans from a popular manufacturer and limit yourself to 3 axis and perhaps a rotary. That's the easy way.
Or, if you seriously want to pursue this, draw it out in CAD, post some pictures of exactly what you want to build, then you will get specific relevant advice, and I'll be happy to throw in my 2 cents.