My son hated being in the carseat, so we rarely used it. He wouldn't sleep in it, and if he did by some miracle fall asleep, he would wake up as soon as the car stopped. So we wore him almost all the time for the first 6 months.
However, that being said, I would still get the infant seat over the convertible - it's safer for little babies. I wouldn't invest in a travel system for the stroller. We got the baby jogger city elite from the start, which reclines fully if you want to put an infant in it, but by the time he would let us put him in the stroller we didn't need to use the carseat.