After the infant seat he moves to a rear facing convertible seat. Some kids even start in rear facing convertible seats and never use an infant seat, so there's no reason you can't start looking for one now. He needs to stay rear facing until a bare minimum of 2 years old, preferably he'll get to 3 or even 4 rear facing. When he outgrows his convertible rear facing then you turn him around and use it forward facing.
When he outgrows the forward facing convertible you have two option, which will depend on his age and his maturity. If he's over 5 and can be trusted to sit correctly 100% of the time he can go to a dedicated booster seat, which uses the car seatbelt to buckle him in. If he's 3-4 or not mature enough to sit in a booster then you will buy a combination seat, which is a forward facing only five point harness then becomes a booster once the harness is outgrown or he is mature enough to sit correctly.
Carseats are outgrown rear facing when you hit the weight limit OR when there is 1" of hard shell over their head.
Carseats are outgrown forward facing when you hit the weight limit (this is very rare) OR the tops of the ears are even with the top of the carseat shell OR the shoulders go above the top harness slots.