I agree about the computer
You've got to get over the idea that you can only have one. And a laptop's not really well-suited to running a CNC machine anyway - they have too many power-saving features (that make it quit working when you need it to) and rarely have parallel ports (which most CNC control programs require.) Get an old beater desktop, strip off everything that's not needed for CNC operation, and dedicate it entirely to running your machine.
As for the ballscrews - it's not true that every ballscrew has no backlash, or is more accurate than every acme screw. Ballscrews do have less drag than regular screws, but that's all they have in common. Some ballscrews were designed for simple motion-control tasks, like opening garage doors, which require little accuracy. They can be shockingly imprecise, and have a lot of backlash. There are precision-ground preloaded ballscrews that are very accurate and don't have appreciable backlash, but they tend to be quite expensive. And there are spring-loaded anti-backlash nuts that can be used with acme screws that will eliminate backlash (at least until you overpower the spring.)
You say you're a hobbyist, but haven't specified the limits of that. If your hobby is building machinery, then sure, you definitely should try building a CNC machine. Even if it doesn't work too well, you'll have had fun and learned a lot. (Of the plans that are available, I like the MechMate best: MechMate CNC Router - Build your own with our detailed plans ) But if you're mostly interested in making wood chips, then just purchasing a machine that works makes more sense.
Andrew Werby
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