How much should I expect to put on one of Beijing transportation smart cards for a family of 4?

If you take the bus, one card is OK. If taking the subway, each of you need a card. As for the expense, you can top up each card with around CNY200 for the first time. If it’s not enough, you can keep topping up the card. If you don’t use up the stored value, you can ask for a refund.