If you use the plastic you won't need the preemergent. However the plastic smothers the soil so I wouldn't use it anyway. If you like the herbicide use it according to label directions. Including recommended timing, what planting situations are suitable for its use and what rate of application it states, which probably isn't "a lot".

To control weeds effectively you have to know what they are. Preen prevents germination of seeds and is applied prior to that. It wears off in a few weeks and has to be repeated for next round of emerging seedlings. It will prevent any germination of seeds you want to germinate, whether direct or self-sown. My strategy would be to wait until the seeds appear and identify them (here on Name that Plant). Then plot your eradication plan. Mulch is your friend, so apply it thickly as soon as you can identify what's what. That could be now.