Hi Mark,
Ok first off let me say straight away that Clive is correct with 3K you cannot build the machine you describe or one that is any good.
When you get into 8x4 or above the game changes in lots of respects and cost is one of them.
Now regards your idea of farming out the welding to engineering firm then be careful because I've seen this done many times and fail.?
The problem comes from the fact most welding firms will weld the frame up as thou it's just workbench and CNC frame requires more careful approach.
They won't take the time or care to spread the welding so as to keep distortion to minimum. They also won't constantly monitor any twisting that might occur from the heat. And most certainly won't take the time to make sure the Rails surfaces are on the same plane.
Any distortion or twist will have to be dealt with later otherwise it will affect how the machine performs. So anything that can be done to lower this the better and this takes time and most welders haven't got the time to wait for welds cooling etc so will just weld it up in one go which will cause you issues down the line.
The rail surfaces must be on the same plane and will need careful attention when welding or they will cause you lot more work. Even then if carefully done your still going to have either Epoxy level or have the surfaces machined flat.
Don't be fooled into thinking Box section is flat because I've yet to see one that is and certainly not one nearly 3mtr long.!
Now regards Gantry and 10mm plate in L shape layout then forget it.! That's just not going to be strong enough for gantry that will be 1600mm wide.
To give some idea the last 8x4 I built which you'll see in pics uses 120x80 HD Aluminium Profile arranged in L shape and I consider that a Minimum for a machine this size.
It's not just the weight it's carrying but got to also think about resonance/vibrations that will occur from the cutting. Resonance will give poor finish, cause excess tool wear and shorten component life.
Next comes linear motion. If your wanting Ballscrews then you really need to know what you're doing and what to buy because when you get past 1500mm things get wobbly real quick.
First, you have the obvious thing to deal with which is screw Whip from the long length. But you also have to think about alignment because long screws are merciless when comes to alignment. The slightest misalignment and they'll turn into gyrating skipping rope which will cripple the machine performance.
Getting this right is a careful balance of selecting the correct ballscrew with regards pitch and diameter along with correct tensioning and alignment. Get anyone one wrong and your in for world of pain.
This why Rotating ballnuts are often used for long lengths but this gets expensive and complicated unless you can make them your self.
Rack & pinion is the common solution for machine this length but again this brings with it's own challenges and problems/costs.
Coupled with all these solutions comes correct selection Motors/drives etc and is one of the reasons why you cannot build a machine this size for £3k.
Long, large diameter screws require bigger motors which along with high power drives get expensive quickly.
Ballscrew or R&P there is no difference really here because R&P is less efficient so still requires large motors to compensate. You also then have more backlash to deal with from R&P. Also R&P will require gearing to give you the Torque and resolution required which adds another layer of costs/complexitys.
I Strongly advise you to think long and hard before you take this project one with No experience because it's very very easy to get it wrong and all the research in the world won't prepare you for just how much more of challenge it is building an 8x4 than say 4x4.
The extra length really does change things that much and the slightest errors get magnified.
But one thing I can 200% tell you is that cannot be done properly or legally for £3k.!!
Here's two for you one with R&P and other with Ballscrews and mounted vertical.!
Attachment 23837Attachment 23838Attachment 23839
https://www.youtube.com/watch?v=4STVbn_EMoc&t=17s