It depends on how much you want to get into couponing. If you want to be like those people that you hear who get like $100-worth of groceries for under $10, then 1 Sunday paper, plus internet printables (IP) will not be enough. If not, then your Sunday newspaper and the occasional IP will be fine.
But, my suggestion is to mainly get the Sunday coupon inserts -- from the largest paper near you, because it will usually have the most/better coupons than the other papers. And, in order to really take advantage of the deals you will need more than 1 copy of those inserts. That means you will need to either buy multiple copies of the Sunday newspapers, or get them by other means, like friends, family, neighbors etc.
Then, supplement these coupons with the IP. One thing to remember about the IP is that they usually expire 30 days after you print them, so you have the weigh whether you think you will use them soon or, if not, whether the link for the coupon will still be there when you do need it. Don't rely soley on IP's, mainly because many stores limit IP's or have some kind of policy against them. Hopefully you will find stores around you more coupon friendly.
Then after all that, in order to use your coupons effectively, choose a site that has forums for the stores you shop at so you can get "in" on the deals.