I would scan at the max of 600 dpi - however if the print resolution is so low that printing artifacts are visible at this resolution (e.g. small colored dots), then the result should either be downscaled or a median filter should be applied to eliminate them (or both). Don't go under 300 dpi no matter what or you won't be able to use them to reproduce new prints at 300 dpi later, which is the lowest dpi suitable for printing.

If you have access to the original negatives, consider scanning those instead using a high-resolution negative scanner (typically at least 1800 dpi) - they can be inverted and printed easily in software and you don't lose quality from the printing process.

In serious archival efforts, 16-bit TIFF is commonly used, and the image is scanned using a high-quality scanner along with a frame with color splotches for color calibration. In home applications, this is usually dramatic overkill. Although PNG preserves more detail and is not actually that big, high-quality JPEGs are visually indistinguishable (barring very close inspection), and are more compatible with photo-sharing websites and applications. Stick with 90% or higher quality JPEGs (your scanner may use a 0 to 10 or 1 to 10 or some other scale - just pick something close to max). It's important to ensure your scan isn't overexposed (or underexposed) because clipped data is irrecoverable.

Edit: One option to avoid the risk of clipping is to scan a 16-bit TIFF with no under- or overexposure as your "archive" copy, which will tend to look dark and low-contrast, and then edit in software to generate a high-contrast nice-looking JPEG for general use.

Finally, remember that you haven't archived something if it's sitting on one disk. A disk will inevitably fail. Either store the images somewhere online in their full original resolution, or put them on a second storage device (second disk, flash, CD, DVD, etc.), ideally in another geographic location in case of natural disaster. If it is stored offline, it should also be periodically refreshed (say every 6 months) by copying it to another device and then back (or to a new device) - otherwise the data will gradually become corrupt due to media degradation.