I'm not keen on attaching flexible hoses to rigid lines without support at the connection between them.
All the piping in the Mini is standard 3/16" Brake Bundy Tubing. I'd suggest avoiding Copper Tube here.
Most of the fittings are as Nick said 3/8" UNF however those on the Tandem Master Cylinders and the bulkhead mounted Regulator are M10 x 1.0. Beware - the 3/8" fittings will screw in to these Metric threads, but don't have enough thread engagement for safety. Try a good wheel nut on the original tubenut, if it goes on, it's 3/8" UNF if it doesn't, then it's highly likely it's M10 x 1.0.
Get decent tools, especially for doing the flairs. They type that have the 2 thin bars with multiholes and a screw press are usually rubbish (I haven't seen a good one yet).
If you are only likely to do say 1 or 2 cars, this is a good tool https://www.carbuild...e-flaring-tool though, look around, as similar ones pop up on ebay and the like.
I'd also suggest getting a tube straightener as when you buy the pipe, it's in a coil. You can straighten it by hand OK, but it never comes out nice. Using a straightener will get them dead straight. This is a cheap one that's ~ OK ~ https://www.carbuild...raightener-tool though, if you are a little handy, you can make one for a few dollars.
A Tube Bender will also let you make nice bends.
I rather enjoy doing this type of work. Take your time with it, making a template sometimes is a good idea in welding wire. When I do them, I start at the end with the tightest bend or the end that needs the most work or is critical in some way, fit the tubenut, do the flare do all the bends, cut to final length and finish the other end.
There's 2 types of Pipe Flares n the Mini. The most common end is what is often called a 'ball flare' and these are what's done on all the tube nuts. There's also 4 Invert Flairs, which are made with the same tool (usually!), first making a Ball Flair, then a second operation to invert the Ball. These are for the Female Tubenuts that connect to the Flex Hoses for the swing arms.