Is the head start step up summon worth or should I just keep my economy growing?

i forgot which one regenerates and which one has a set limit per match but you can regain some back through items. You have to select them prior to starting the match.

how do you replenish ap and tp

Depends. You're spending 4500 to get the guaranteed UR at the end. During those three step up pulls, you have the chance of getting multiple UR. If you think that the 4500 can be spent elsewhere and get you other UR, you can save. But just remember, if you spend your currency elsewhere, you may very well not get a UR - that's why most guides are saying pull from the step up summons since they are discounted.