For this purpose, an important characteristic of a camera/lens combination will be how well corrected it is for rectilinearity (straight lines stay straight), vignetting (avoiding bright center and dark corners), and, to some extent, flatness of the focal plane (so that the center and corners of the image are in focus at the same time). All of these become much more important for images of flat surfaces that are going to be fit to each other (tiling) and to regular polygons such as 3-D models of interiors.
Lenses that correct these well can be large and expensive, but there are ways of mitigating the problems in software, and many current fixed lens cameras (and at least one interchangeable lens system) actually software correct the first two in-camera, facilitating cheaper and smaller lens design. Some recent cameras are even capable of internal focus stacking, which can address the third issue. Most in-depth reviews of lenses (or fixed-lens cameras) will give at least some attention to these characteristics, so that's what you'll want to pay particular attention to.
Another thing to consider is whether the angle of view of a camera/lens combination will allow you to capture the area you need from a distance that works with your lighting and space constraints. The old macro lenses mentioned in another answer, when used on a typical APS-C DSLR, will have an angle of view similar to "zooming" your phone to 3x or more. If that seems to work for your purposes (and you don't mind manually focusing) that could be a good option.
If you find that cameras within your budget produce images that could still use additional correction (not unlikely), there are many software packages that can help with this. One popular free software project capable of many corrections is hugin, but other commercial software may offer a gentler learning curve.