Mage Wars Arena core set is just the 4th edition of regular mage wars core set. There are slightly different card counts of each spell compared to the 3rd edition, but for the most part they're the same. Adding "Arena" to the name was just rebranding of the regular game to distinguish it from Academy. You already have more than a decent enough collection to do well in organized play. If you want to get something more, my advice would be to just pick what you and/or your playgroup would most like.
If you want to play more mage wars even when you don't have an hour or two to spare, I think Mage Wars Academy is coming out at Gen Con. That will probably cost around $30 for a set. I don't know if they're first releasing Wizard vs Beastmaster and then Priestess vs Warlock later, or vice versa or at the same time.
Mage Wars academy is basically like arena but with only 1 zone, different spells and younger alternate versions of the arena mages with their own stats and unique abilities. You can't attack or cast spells on enemy objects for the first 2 rounds. The spells in Academy can be used in Arena, but not the other way around. Because of the differences I just described, the strategies and metagame that we end up seeing will likely be very different from arena, so even if the rules are otherwise quite similar, the gameplay should probably still be different enough that they both stand on their own merits. Also, Academy is much more portable.
I tried it at origins and I highly recommend it to anyone who wants to play mage wars more often but feels like they don't have as much time to play it as they would like.
EDIT: Boocheck ninja'd me on some of this.