Use a tripod
A tripod will allow you to use the lowest ISO for the best image quality, and a long shutter speed to gather enough light, no flash necessary. Using a tripod will allow you to use any camera, even a point-and-shoot, with very good results.
If you are unwilling to use a tripod, you will want a camera with as big a sensor as possible, and as wide aperture a lens as you can get. A camera that also does in-camera HDR would be handy as well. There's no law that says you cannot buy an interchangeable lens camera and just use one lens; an entry level DSLR with a wide aperture prime lens would be the cheapest way to get the best performance...far cheaper than the aforementioned RX1.