Some general recomendations.
1) The resolution of the file.
You need at least 150 ppi for this. At 3 ft you need 3x12x150=5400px on the long side. So you need a 24Mpx file at least.
2) You want a sharp lens.
Try a Prime lens for this. The longer focal length the better becouse you reduce barrel distortion. Lets say an 85mm.
3) Good ilumination.
a) You need an uniform lighting, for example 2 or 4 lightsources at 45 degree angles. Probably difuse light.
This is not mandatory becouse you could have the case the painting has a lot of 3D texture, like rocks or sand, then you need to play with the light and shadow.
b) You should prefer a continous light source with a good spectrum. Avoid fluorescent lamps if possible. https://www.google.com.mx/search?q=continuous+light+spectrum+fluorescent+vs+led
4) Incident light meter.
For a more precise aproach you should measure the light with an incident light meter. The light diference should be less that 1/2 - 1/3 stop on all the original paint.
There are some sekonic models that allows you to find the real tonal range of your camera. https://www.google.com.mx/search?q=sekonic+find+tonal+range+camera
5) Calibrate your workflow.
d) You need a color chart target like this one: http://xritephoto.com/colorchecker-passport-photo
e) Color calibration hardware like this one: http://www.xritephoto.com/custom_page.aspx?PageID=299
f) or a more pro solution like this package: http://xritephoto.com/ph_product_overview.aspx?ID=1913
So. Calibrate your camera. Calibrate your monitor. Calibrate your prints.
(It is usefull to prepare a custom white balance inside the camera, but as you are using the raw files it is not completly necessary)
6) Use a good monitor.
7) Shoot in raw.
Look for tutorials on how to manage a well calibrated workflow with the previous equipment. https://www.google.com.mx/search?q=xrite+color+checker+workflow+tutorial
In this case you need to use Adobe Lightroom becouse you can use the color profiles given by the Xrite calibration hardware and targets.
Use the ProPhoto color space. https://www.google.com.mx/search?q=adobe+prophoto+color+space
8) Use a tripod.
9) Use a good printer
This is another topic by itself, but you want photographic quality prints, probably latex based ones. You need a service bureau that allows you to make some tests, and if you come the next day they mantain the same configuration on the equipment.
Use this recomendations as starting point to find out more. Yes... you have homework to do.