There's a number of reasons to consider about using the access you have to the CNC.

the 1st is MDF is horrible stuff to work with ... I hate it ! LOL. (make a living with it, but hate it ! )

but,
you get to start using software to draw parts out and convert to gcode - you'll need to learn this before you can use your finished machine !

you will get accurate , straight, and square parts, and the holes will be neat and line up with other parts that have to fit together.

You can get a bit creative with the design. The Z for example, can be a complex part to make by hand. The router and Vac mount is easier to cut by CNC etc.

I'm just saying consider it, if you hadn't , that's all. Nothing wrong if , like you said, you want to get stuck in and make it all by hand.

I built mine by hand, but I thought I was going to use it to 're-build' itself, once it was running. Turned out to work just fine, so it's still as I 1st built it .

When I build the next one, I will definately use the 1st one to build the next.

There is still the 'fun' in doing that. It's sort of like using the tools you have available to you, or borrowing some that would make the job easier..
You could use a hand saw and bit and brace, through to a table saw and pillar drill, or all on a CNC machine ! you are still making it, but with tools at your disposal. Think of it like borrowing a jig saw (or router! )to cut some parts for instance.

do you have a start / finish date in mind ? As your mate has already build one, what about elctronics and motors ?

What software do you think you will use ? I use Linux, because it's free - and I like that philosophy :) It runs on a prety old and basic del pc I had lying around.

Rich