I think you get the msg about the working for free thing...
If you can afford to do it then I would go flying first...you're right, you'll have more hours that way and be able to go to an airline straight after college. Age will be more on your side too as you won't need to waste more time in the wilderness building hours. Also, if for some reason you decide not to pursue a professional flying career after college, you can go straight into a "conventional" job but keep instructing as you wish as a hobby.
Also, you'll be the coolest person in your class if you work as a flight instructor while everybody else is pouring lattes or flipping burgers.