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If you read these forums and tier lists, you will get a general idea of which champs are better for dominion.
Take advantage of free rotation and play the heck out of the free ones till you find ones you like.
As luck would have it Ryze is free this week. Play him with this build:
Try to get as much CDR as you can from masteries/runes. 9-0-21 is ideal for 10% starting. (then 6% more from blue runes you probably dont have)
Tear, boots, 2 pots. Can go bottom or top.
rush a Glacial Shroud to boost armor, mana, CDR.
upgrade to Sorc Shoes
upgrade to frozen heart for mad armor, maxing your CDR.
get negatron cloak
upgrade to Odins Veil
From here, get a Rod of Ages as a good general booster. Ryze has quite a few viable options at this point, but Rods work well for general purpose offense/defense.