Hey there! I bought one of those "car seat strollers" (the Graco Snugrider) and loved it. Inexpensive and very convenient. When my son was about nine months old, we switched him to a new stroller (bigger & forward-facing) but still used the Snugrider as his car seat. When he turned one, we bought a new car seat (forward-facing). This may seem a bit wasteful, but that car seat and stroller were beat to death by the time we replaced them, so I feel OK about it.
When it comes to toting your baby around, if you are athletic and like being mobile, I suggest the Ergo and / or a wrap. I tried slings, wraps, etc, and none of them were very comfy until the Ergo. You'll need the infant insert at first if you use the Ergo right away. No big deal. If you want to try a bunch of different types of wraps, go to one of the two Pump Stations in LA (either Los Feliz or Santa Monica). They offer a freebie class once a week where pregnant ladies / new moms get to try out a bunch of wraps.
Graco Snugrider was great for just getting around (especially when the baby is sleeping so much) and the Ergo was great for bonding, walking, having hands free, and so on. BTW, I am not totally sure what you mean by the baby "lying down." He sort of reclined a bit in the Snugrider, but he was still sitting up. And I liked that he faced me in that stroller as opposed to facing the outside world. Developmentally, that is supposed to be a good thing. (I'm sure next year they'll tell us that developmentally, it's a bad thing! Ha ha! But for now, facing mom is the way to go.) Good luck to you!