Infants and toddlers should only be in rear-facing or rear-facing convertible car seats until they're at least 2 years old, or reach the threshold for weight or height designated by the car seat manufacturer—whichever comes first.
Toddlers and preschoolers should have convertible car seats, and if they have surpassed weight/height limits, can be in a forward-facing seat with a harness. They should stay in these seats for as long as possible until they max out on the weight/height limits before moving into a booster seat.
School-aged kids (kindergarten and up) who exceed the weight and/or height limits of a forward-facing car seat with a harness belt should ride in a belt-positioning booster seat until they're big enough to properly use a regular seat belt. And for the record, your child should be at least 4 feet, 9 inches tall before they're "too big" for a booster seat. Although they may be tall enough or heavy enough between ages 8 and 12, they should stay in the back seat until they're 13 years old.
Older kids should use lap and shoulder seat belts, regardless of whether they sit in the front or back; but they should only be sitting in the front if they're older than 13 and have exceeded height and weight for booster seats.
When in doubt, consult the instruction booklet for your car seats (you can get them online from most manufacturers if you have no idea where they are) or call the manufacturer and have your make and model number available to get guidance from their consumer help line.
Here's a handy chart you can save to your phone for the next time you're car-seat shopping:
Photograph by American Academy of Pediatrics
Find a 2017 list of car seats with manufacturer name, make and model, weight and height limits, as well as prices available from the AAP here. The list includes rear-facing only seats with 5-point harnesses, rear and forward-facing convertible seats with 5-point harnesses, 3-in-1 seats that can be used rear and forward-facing, or as a belt-positioning booster, forward-facing combination seats with a 5-point harness or belt-positioning booster, belt-positioning booster seats, and a few other options you might be considering.
Because laws can vary from state to state, it's best if you follow the most stringent safety guidelines. The AAP notes that there is no one car seat that is best or safest to buy; rather, the one you should use is the one that your child fits into properly, is correctly installed and is used properly every time you get in the car. Although car seats can range in price from affordable to very expensive, the price tag with a higher number doesn't mean the seat is safer or easier to install and use than a more affordable one.
The car seats you shouldn't use? Ones that are expired (usually six years after the date it was manufactured), ones that have been in accidents (even if the car seat itself doesn't appear damaged) and seats for which you don't know the history (something to watch out for if you're purchasing a second-hand car seat).