Is it better to get an infant car seat or a seat that converts from one stage to the next? Is there any benefit to the infant car seat that justifies paying for an infant car seat and a toddler car seat?
Better for your wallet: the convertible.
Better for your infant's spine: the infant seat.
The Austrian automobile club recommends to use infant seats for infants and not convertibles and my wife who is a trained physio therapist explains why: infants' spines are not fully developed, which means that infants should never sit or even recline until they are able to sit by themselves. Only then do they have the muscular strength that we adults aren't even aware of to keep the spine from collapsing on itself.
This medical opinion might be different in your region, so I would recommend that you ask your automobile club and/or your pediatrician or physio therapist if you have one.
The automobile clubs in several countries I know actually offer approved infant seats for rent at ridiculously low (symbolic) rates. That made our decision for a (rented) infant seat and a (self-bought) child seat very easy.
Getting a convertible car seat saves you money in having to purchase two seats, but I would recommend an infant seat. When you first bring that little peanut home, they are so tiny and dwarfed by any car seat. The infant seat has them in a reclined position that I have not seen in a convertible seat. When my son was a little over a year and we were preparing for the birth of our second, we purchased a convertible seat for him that goes up 65 pounds in a five point harness and then to a booster till he is 100 pounds. My favorite part is that if they fall asleep while running errands, you can take the bucket out and get things done while they sleep on. I truly missed this feature when my son outgrew his infant seat.
We bought a stroller that came with an infant seat which made it really nice because the infant seat locked right into the car or into the stroller without waking our son.
The infant seat lasted us a while too so we did not have to buy a car seat for a while. If I remember correctly the seat was adjustable so it could sit upright a little bit making it work for us longer.
There are pros and cons to each:
If you buy an infant car seat, it can do things like attach to shopping carts and strollers so that you don't have to move and wake your baby, and acting as a standalone carrier or rocker when you travel. I don't know of any convertible car seat that can do these things.
If you buy a convertible car seat, you forgo the features mentioned above, but you save money, having only bought one seat.
The infant car seat is a much safer option for newborns than the convertible car seat and can typically support a newborn as small as 4 pounds, whereas the convertible starts at 5. This could make a difference for newborns with low birth weight/preemies. You shouldn't place the infant car seat in anything for which it wasn't intended, though, such as a shopping cart.
A couple years ago I was in a parking lot and a woman parked near me had her infant in the car seat sitting in the front portion of the shopping cart. As she was loading the cart with items from her car trunk, the cart tipped completely over and the infant landed upside down on the ground, still strapped to the cart.
The infant was wailing, and I watched, horrified as the woman picked the baby up, looked at him for a few seconds, and then went into the store to shop. I assume the baby ended up being okay, but it's not worth the risk.
You do need to think of practicality as well. We opted for a high end convertible seat so we could use it for much longer. From the reviews and safety ratings we were satisfied it was just as good as the infant seat. The infant capsules only last until around 6 months.
It's of much greater importance to be aware of your driving, and always drive cautiously.
It's much much better to do everything you can to avoid getting into an accident in the first place.