Ok straight of the bat drop any thoughts of building from wood as you will regret it and defeats the point in using components like linear rails and ball-screws. It will also cost nearly as much if not more in wood than it would steel and take longer to build.

Next is the 5K. Yes it's just about do-able building your self but you'll need to be careful with what you buy and nearly all the major components will have to come from China.

Regards how to drive it then this needs careful consideration, esp if you have little to no experience because when you get long things begin to get complicated fast.
R&P is often used on large machines but it's the least efficient typicly around 50/60% with more backlash so it needs large motors/drives etc which cost more and needs the most maintenance.
Gearing will be required so you need to factor which method to use and what ratio will be needed to give you the feeds you require and keep the motors in right RPM range to give torque while cutting. Get it wrong and you'll be chasing speed or constantly chasing issues with stalling motors and belts etc.
The setup is simple but needs most maintenance adjusting the backlash to a minimum while at the same time not over tensioning the pinion causing excessive wear.

Rotating ball-screws are far better-regarded efficiency typically around 90-95% and require slightly less power but they come with there own issues, namely screw whip at higher feeds. So again a careful selection of right screw diameter and pitch is required along with motors. Thicker screws whip less but the inertia is a lot more so more powerful motors are required, again more costly. Alignment also requires careful set up so there's more to setting up the machine. The upside is that when it's done it's done unless you have a major incident and skew the gantry up badly, in which case you usually knacker the screws anyway so it's all fubar.!

Rotating ball-nut setup works the best in my experience but these are not something you can easily buy of the shelf and very expensive. So the only option is to build your own which isn't something most people can do unless they have access to a lathe and mill and know how to operate them to hold high tolerances.

Next option and one I'd suggest you consider is using a belt drive.? It gives a combination of Screws and Rack. It's very efficient at around 80% with low backlash and if done correctly can give very close to the ball-screw performance. It still requires gearing to give you the correct feeds etc but with much less hassle than R&P gives regards setup and adjustment.

Regards the rails then 20mm will easily handle the loads etc but 25mm works better on a machine this size and to be honest, the difference in price isn't massive so not worth not using. Highwin Linear rails can be joined easily enough but you can buy them up to 6mtr in length in the UK. From China, 2,9Mtr is about the longest you'll get if using air freight. If you ship them by sea you can get longer lengths but is a pain in the arse and takes longer.

The goal when building a machine this size or any machine, to be honest, but esp at this size is lowering vibrations because they affect the performance and finish also increasing tool wear. So with such a wide machine, the gantry becomes a tuning fork. So a substantial gantry and rail system pays off big time.
Don't let the fact your cutting MDF and Ply fool you, to cut correctly and make machine this size worthy you'll need a strong gantry with a spindle that can handle a good depth of cut at correct feeds. You'll also need a good dust extraction system so factor this into your Budget.!

Regards the spindle then you'll need a Z-axis Motor with a brake otherwise it will fall under its own weight when powered down or strain the motor when at standstill for long periods. These things are all adding to the costs and highlight just how quickly costs can rise.

My Strong advise is to buy NOTHING until you have finalized design to a relatively high level with a full understanding of what building and why you are using those components. If not then you'll just blow money, waste time and frustrate your self daft when things don't work as expected.