The Chicco base is only for the infant seat. The extra base is a convenient feature if you regularly use several cars to travel with the baby but it would become obsolete when you switch out of the infant seat, which usually happens before they hit the max weight limit of 30 lbs because of height. We moved DD out of her Chicco infant seat at 10 months.
As far as I know, Graco is the only manufacturer that recently introduced an extended use infant seat that you can use until 40 lbs RF, which should get most babies RF to 2 years old as recommended by safety experts. It comes with a separate base.
As for the convertible seat, you'd be starting from scratch since you will need to consider budget (possibly 2 separate car seats), fit in your car, ease of use and whether extended RF is important to you. Some of the most popular and recommended models are Graco My Ride, Britax Marathon and Boulevard/Pavilion, Diono Radian XTL and First Years True Fit and they all have different pros and cons.