S.A.
First of all, you should never buy a car seat second hand unless you get it from someone you know. It is recommended you buy a new one (they actually "expire" after a while) - it is well worth the extra money for the peace at mind knowing that it has never been in an accident or been recalled.
You need to make sure that your car seat is ok for an infant. Also, you need to have a seat that can go rear facing until he's at least 1 year old AND 20lbs - and actually, the longer you can keep him rear facing the better! The car seat instructions should tell you the weight and height limit for the rear facing position and only once baby exceeds that you should switch it to front facing (if it CAN go front facing -if not you'll need a new one that can. Some seat are good for both position, some are just for front facing, some are only rear facing...)
If you want a separate car seat and stroller or not is up to you - it's all in your preference.
Be sure to do your research and make sure you have the right car seat for your son and your car, and that it is properly installed - it is for your son's safety!