First have a read of
Jukka Aho's "Quick Guide" then ask yourself whether this is really something you want to deal with properly (bearing in mind his is a
brief explanation). This should also explain that there are two different ratios to consider here, the image aspect ratio is not the same thing as the pixel aspect ratio, the IAR tells you the shape of the video, while the PAR tells you the shape of the pixel distribution or pixel grid within it.
Section 3 has a large conversion table that gives the correct conversion factors and to answer the other part of your question, yes, do the resizing before you transfer it to your Axim as that way you know the conversion is correct plus it will display correctly on a PC monitor.