The only problem with "flight training on the side" while you are in college, is that you won't be able to concentrate on it. It will therefore cost you more probably as you won't be able to fly often enough to cement those core skills.

I would recommend getting a job over the summer while still living with mom and dad. Fly every day at your local airport, and make sure you keep up with all the ground work. Personally, I don't recommend doing a ground school first as you have nothing to correlate it with. Another option is to get your sport pilot certificate first, then add on the private pilot. Joining ROTC or the Civil Air Patrol may give you access to military flying clubs, which are cheaper, at bases in your area.

Finally, there are a lot of hucksters in flight training. Don't pay too much up front (to get a discount, for example) and don't get talked into some ab-initio program at this stage. Just concentrate on the private certificate first. Be forewarned, this is a very expensive pursuit which does not pay well.