My advice for a long time has been to buy a truly "fast" short telephoto, and then later crop the images at the computer. My lens recommendation is different from what many people recommend,because there is more than one way to shoot football, and you're shooting for 'memories', and not for a daily newspaper or weekly magazine. "Modern" football photos are in many ways, very poor recordings of the games and plays and players, but are instead, very often limited to very close-in, half-body shots that feature one or two players at most. Professionals shooting 300,400, and 500 and even 600mm lenses are forced to take very small segments of the game. There's no "context" really, it's all provided by captions that say, "Running back so and so scored on this third-quarter off tackle run to tie the score at 14-14," and so on.
My advice: if you do shoot from the sidelines, stay 7 yards ahead of the line of scrimmage, and stay alert, and shoot with an 85mm f/1.8 AF-S Nikkor lens, and CROP later. The D3200 has a 24MP sensor...it shoots high-resolution images, and you can throw 50 to 75% of a well-exposed, crisp frame away, and still make a good picture. Seeing OLD football photos, like those shot in the 1930's through the 1960's, you can actually SEE "the plays", complete with both lines, complete with burned defensive backs and befuddled linebacker crews, on TD passes...you can see some actual CONTEXT of the games...
A breakaway dive play off right tackle from the stands shows the lines, and the RB as he scampers thru open field, the goal posts in sight in the middle of the image...the "professional's" 300/2.8 shot from the 20 yard sideline shows a single, isolated kid, running in space, with NOTHING else....there's no picture worth a damn--but it makes a good caption!
Spend the $400 and get the AF-S Nikkor 85mm f/1.8 G lens. That is the ONLY lens you can afford that will actually be useful AND which will allow you to shoot at high school fields, night or day, at High ISO values like 1600 or 3200, and at f/2 and 1/500 second at night. You need the G-series model for autofocusing on the D3200. A lot of football happens as plays come right toward the sidelines, and in the endzone areas, an 85mm lens is plenty long enough. FORGET shooting football the modern "professional" for-publication way, and show some context, and crop-in on images you want to be closer-up. It takes way too much practice and skill and big glass to shoot football the "professional" way, which is tight,tight,tight framing...so do it the old-fashioned way, where the game is shown more within the context of seeing 5 to 15 players, or seeing breakaway scores with more players, more field visible. And then if you need to, CROP later!
Shoot looser, with a TOP-quality, high resolution lens. The 85mm f/1.8 G series is one of the ten sharpest lenses in the world, even at its low cost of $405.