This is actually non-trivial. If there was only one wavelength, and a source that was very small, it could be solved with a single lens that has the source at it's focus. For the rather tough requirement of collimation over 500 mm a best form (bi-spherical) lens might not be sufficient and an asphere or multiple lenses be required.
Now the white light requirement makes this much harder. To make sure that rays of all wavelengths are bent the same way, you need an achromat (correct at 2 wavelengths in the visible) or better and apochromat (correct at three wavelengths in the visible).
A Fresnel lens is unsuitable, because it is typically of too low quality and is not color corrected. Also the transitions between the 'blazes', i.e. the areas that have the wrong curvature, really mess up the quality.
Luckily people have been building lenses that can do both the low aberration focusing and the achromaticity, because the requirements for visible wavelength photography are very similar. I would look for an existing used fixed focus camera lens. Zoom lenses make too many compromises to be good for this.
Generating a small, bright, evenly illuminated light source is a separate problem, which might require a very bright source, some diffuser or homogenizer arrangement and another achromat or apochromat.