CNC for under $1000

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The biggest problem with buying a small machine to start with is you will probably find the limited small size inadequate for the projects you will want to do. I have also found that using some of the free software packages available to add to the limits of what you can do. If you encounter too many limits the problems can be overwhelming and lead to giving up before you actually get started.

That being said, I also realize you have a budget and will want to stay close to the funds available to buy this new toy. I would recommend the same CNC that Tagwatts recommends but the price is $1200. That does inlcude Vectric VCarve Desktop design software which I also recommend. This will be a tighter machine than most of the others and to do projects like the hexagon tile game board you will need a good tight machine to make sure all the parts fit. The big plus to this machine is the upgrade program so you can upgrade to one of their larger machines later. I think it would be well worth checking into. Next Wave CNC

CNC.. is not a cheap endeavor... and usually when you get sucked in.. it gets even more expensive..
If you want to reduce the cost, you are going to have to go the diy route, you get far more bang for your buck, but you also risk screwing up and making an expensive mistake....

Another option.. many Makerspaces have CNC machines (and 3d printers and a bunch of other things), and they usually have the staff of volunteers that will help you learn.. before you make any investment..

All that said.. if you want something nice for under 1k... you are going to enter the DIY realm.. These machines are not that difficult to build. There is the PRINTNC which is extremely rigid (it's made with steel rectangular tubing and Aluminum plates, as well as some 3D printed parts. Total cost with an electronics package (at your price point you are going to want an all in one, something from openbuilds like the Blackbox, or an arduino with GRBL flashed and a stepper shield) could easily stay under $1k.. But you are going to have to build it yourself.

Keep in mind.. once you get a machine.. you are always going to hit it's limits, and most of these hobbyist/diy/low budget machines... have limited Z range, usually 2 to 4 inches (thickest material stock you can fit under the x gantry), which may limit what you can machine. Once you go larger, the hobby/budget machines start to lose accuracy, anything up to 0.5mm on the Z is a possibility.

If you can push your price tag up to 2k, you can pickup a pretty decent machine, also in the hobby/DIY range, you could go with almost any of the Openbuilds machines, or the New-Carve (NEW-Carve cnc machine) and an electronics package.
The New-Carve uses linear bearings and ballscrews which will provide significantly more accuracy (even if you use the budget ones from various sources) over some of the other options (v wheels suck.. I have it on my lead 1010.., belt driven, and other methods of providing linear motion).

As far as skill level.. if you can follow a youtube video.. assembly is pretty straight forward (all of the openbuilds machines have extensive video instructions, and the new-carve comes mostly assembled to begin with)..

Full Disclosure: I have no connection to any of the products I mentioned other than being a user