I've built a few belt drive machines now and can I say while they work very good they don't workout any cheaper than machines with ballscrews bought from china. By the time you have applied a ratio needed to get decent resolution the cost of good quality pulleys and belts required is the same or if not more than screws from China.

The cheap class 7 ballscrews are much better and far less hassle than even good quality belt drive with better efficiency. So my advice is Don't even got there just go straight away with ballscrews you won't regret it.

If you must go with belts then either of your designs will work but you will need a ratio applied, how much depends on the pulley size and resolution required.
One bit of advise is don't go too small on pulley size to increase resolution as the number of teeth engaged is important and smaller pulleys means less teeth engaged so higher chance of teeth jumping and belt wear.