I always buy one or two salted porks on turn 1 for my sovereign, then at once go out with him alone killing monsters one by one. My second hero I use for scouting nearby areas, some garnison duty now and then to decrease unhappiness, and to join my sovereign in every quest I take (quests don't share the experience among the heroes I think). The champion is also used to transport loot I don't need back to the capital to be sold.
After this phase it's unit building time, and one and one hero with his own army going bananas all over the place.
NB! Since your first money will go to salted pork and hire of a hero, the thing you should research first with this start is restoration, and build a workshop asap. You will not need the rush buy ability for a long time. I often go straight for horses after restoration and knowledge actually, if I think I'll have enough money for a horse for my sovereign so early on.