When the family is just starting out money is usually tight. Don't expect to be able to spend money on upgrades for several days, maybe not until the second generation.
The game pays 10% interest a day on the peeps' bank balance, and it's surprising how quickly it mounts up - provided you keep the balance as high as you can.
Make sure you praise your peeps for working, so that they earn regular career promotions and earn more money. Be careful not to over-praise them, though, or they'll tire themselves out. Keep a sharp eye open for collectibles; a regular income can be gained from selling duplicates online which should usually cover expenses like food or medicine for the more minor ailments. That means that the peeps' earnings should accumulate in the bank to earn interest.
Obviously, you can be unlucky and have a series of events or emails where you have to pay out money, but they usually average out over time with the "good" events where you gain money.
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To err is human; to arr is pirate.