I recently recieved parts of my family tree started by my grandmother, where do I go to get the best possible information?

Don't tell anyone I told you, but this is how you do it.
First, you'll need a software program to keep track of all of your information, because writing it down and trying to keep track of it all is consuming. Go to ebay.com, and search for "Family Tree Maker 16". This software includes a one-year free premium subscription to Ancestry.com at no cost, which includes access to all of the U. S. Federal Census images, Immigration listings, and other priceless reference materials, such as books on histories of the region, county, or even city, that you may be searching for an ancestor in. You'll be surprised what you can find in this free one-year membership. The cost for the software averages $19.99 online, with sometimes Free shipping. Always check the comments on the seller, though, to help make an informed choice whether to buy from them or go to the next one and buy from the next guy.
Second, install the software after you get it in the mail from the purchase, or if you go to a store and happen to find it and buy it. You'll have to give a credit card number that is current and valid to get the one-year free ancestry.com membership, but you can cancel before the year is up, and your credit card will not be billed. There is a link at ancestry.com once you log in to view your account, and it will show when your one year is up.
Best of Luck!