I purchased Descent first edition a number of years back but for one reason or another never played it. To play the second edition, do I just need the conversion kit and to download the rules? Or, would it be better to just purchase a new Second Edition? I hope the question makes sense.

You will need the V2 core box for the tiles, cards and tokens, and the the conversion kit to use your V1 monsters and heroes.

The conversion kit is just to give room for your old miniatures in the 2nd edition, monsters and heroes. You'll not use anything other than that from the first edition.