There is a big different between INFANT carseats and baby carseats. An infant carseat usually does not last longer than 4-6 months. They are intended for newborns, NOT larger babies. I can't tell you how many times I go out and see huge babies being carted around in infant seats. It's not safe.
Anyway, a convertible carseat will be the most cost-effective. They can rear-face and forward-face. They can hold a child up to 30-60 lbs, depending on the brand. Britax makes the safest (and one of the more expensive) seats. I personally have Graco but PREFER Evenflo seats.
The convertible car seat I got for my youngest was $70 at Target and has a beautiful flower print on it.
In order to remain in a rear-facing seat, they must be 20lbs AND be at least 12 months old. If they're 20lbs at 9 months, you still have to wait a few more months before you can turn them around.
I would still get an infant seat with a base for the first year. It's so nice to be able to take the seat into the house when they fall asleep and not have to disturb them. I also love just clicking it into the stroller when you're out shopping :)
I had the Graco Snug Ride until my son was 9 months old and then switched to a Britax Marathon seat. They're quite expensive (around $280), but they're the safest seats on the market and are SUPER easy to install (forwards and backwards). Mine is so tight in the seat that if you tug on it, the whole car moves. I like it because you can use it for babies 9-35 lbs rear-facing and 20-65 lbs forward facing. My son just turned 2 and he's 27 lbs, so he'll be in that seat for a long time.
You can get them on sale from Target online and can often get free shipping. I liked it so much that I got another one for my husband's car! I consider it an investment...
My son out grew the infant seat at around 6 months. He was 6lbs 15 oz and 20 inches. He was too long before he hit the weight mark.
With my son he was out of the infant seat before his first b-day but he was a big baby to 8.1 21 inches long so it depends on how fast the baby grows on how long they are in the infant care seat.