Nick,

Welcome to the forum.

I'll try and answer your questions, I'm sure other will leap in with their 2p worth...

'Best' supplier is all relative... what is your criteria? price, delivery, aftersales? If you want a UK supplier with good aftersales then Gary at Zapp has a good reputation. If you want price, then ebay is your friend, there are a couple of good sellers in China.

Ballscrews are hard, but can be machined, you can break through the hardening with a toolpost grinder...

For motor sizing see the tutorial here. While sizing from what others have done is an approach, it usually means oversized motors as generally its all been guesswork, and oversizing is a waste of money and can be less effective - the static torque of the motor has little bearing on its effectiveness as speed and drive voltage have as big a part to play as well. The tutorial will give you some guidance into what your options might be. Ultimately 'it all depends' is often the answer...