There isn't a travel system that meets all your requirements.
I would suggest that you look at strollers that can accept car seats but are not sold as a "travel system" set. A lot of moms ditch the stroller that was part of their travel system once they stop using it with the car seat because the stroller is bulky. Some umbrella strollers can accept a infant seat, so that might be an option since you could use the umbrella stroller when baby is older and they tend to be lighter weight and more compact.
If you wish to run with your stroller, you will need a jogging stroller. Something with big air-filled tires that is designed for running. A jogging stroller doesn't make a good everyday stroller though since they tend to be heavy and don't fold compactly at all. I believe the minimum recommended age for running is 6 months, so you could wait on getting a jogging stroller.
Another option is to get a snap n go stroller frame to use with the car seat, and then buy a regular stroller later on. You could then get a nice lightweight stroller after that.
With my DD, I used a Quinny Zapp with the Maxi-Cosi Mico car seat attached. The stroller seat zipped out so it was basically like a snap n go. it was convenient to have a small maneuverable stroller. By about 6 or 7 months we stopped using the car seat on the stroller. I also have a City Mini as our "big stroller", which we use for all day outings, on unpaved surfaces, and for trips to Disney. I find it too big to use everyday though.