If you have a resonably low income, I wouldn’t suggest going for credit cards with $500 or $1000 annual fees. I would stick with no or low annual fee cards. To maximise points, you want to look at sign-up bonuses on Credit Cards. To answer your question, when the credit card requires a minium spend of $4000 over 3 months to get the sign up bonus, it means that you need a total of $4000 in spend charged to your card over a 3 month period. It can be split into as many transactions in 3 months. As long as you have paid off over $4000 in balances on your credit card, you’ve done it.
For credit cards, if you don’t want to pay an annual fee, I would suggest the AMEX Essentials with 1 AMEX point per dollar transfered to around 0.5 frequent flyer points. If you want something a bit higher end, you could get the AMEX Platinum Edge which earns 3 AMEX points on supermarket shops which you can transfer to 1.5 frequent flyer points. It also comes with a $195 annual fee but that is offset by the $200 travel credit you can use to book flights for you and your son! There are a great range of cards out there so I would suggest doing some additional research into the level of cards you can afford to have with your current income/spending patterns and what benefits you value most in a credit card.