When you load your cleared game, you first appear in the basement of the Empire. Immediately talk to the man behind the table, and choose "He's already been defeated," then choose "Punish." This will get you the Summoning Jewel.
You can also fight the Battle Contraption again, if you want (though I don't think it has any impact on the rest of the game).
Now that you've defeated Papurun, you have the Dark Lord's Gem, which is needed to unlock the final job class - Magical Star.
Whether you're playing the game on Easy or Normal, I highly recommend that you train up each of your characters to a 3rd-tier job class.
Zilva, Tink, Lufa, and Midori are easy, because they each only have one job "path."
For the other 6, you can choose any combination you like, but I went with God Hand for Blont, Bruce, Linn and Claw, and Magical Star for Temi and Mazenda.
Anyway, I recommend that you spend some time training everyone through their various classes before proceeding. You don't have to get them all the way to the 3rd tier right now, but the sooner you do it, the better.
Along with changing jobs, you'll also want to get the best gear available, at least for the 5 characters that are in your "fighting" party. (The Orihalcon gear is great for everybody - but it is expensive and there will be better gear in the bonus areas, so you don't have to go crazy buying it for everyone if you don't want to.)
The best place to grind for Gold/EXP at the moment is the Antarctic Plateau, because the Metal Animals give 150EXP each, and Rare Metal give 500G each. Also, the battles here get progressively easier as you go up in job classes, so you basically get short, easy battles with good rewards. If you want to train everyone to their 3rd-tier jobs, this is the definitely the place to do that.
When you feel that you're ready to move on, the first place you need to go is Arena Town.