Simple enough, use all of the 1-cost units and Twitch for Swiftshot. Since this is a 1-cost reroll comp you want to go on a lose streak from the get go. DON't level up early!
Don't spend your gold until you hit 50 and then slow roll above 50 gold for Ezreal, Leona and Nasus. All the units are low cost, making them easy to pick up. Level up to 6 only AFTER you hit Ezreal 3 star (latest at stage 4-1)