We're like you, a smallish shop that covers a lot of those same things. We've had a handful of guys make it to the NFL over the years, ranging from players who washed out in training camp to one very recognizable star.
For now, I'd suggest getting on good terms with them. Not saying suck up to them, but make sure they know who you are, you have their phone number (and their agent's number when the time comes; the player's number will probably change at some point), and your calls get returned. If you can get on good terms with the family, that helps a lot, too. It'll be a big asset as they're rising up through the draft process and the early stages of their career.
Having them know who you are also helps a ton down the road when you have to go through an NFL team's PR department. In the case of our star player, I know we got at least one phone interview not many other outlets got -- anywhere -- because he likes talking to the hometown paper. I think we're on a list of approved outlets or something. So at some point in their rookie season, try to reach out to their NFL team as well. It never hurts for them to recognize your name or at least the paper's name.
As far as frequency of stories, it depends a bit on their role with the team. I'd say definitely do one story pre-draft, another post-draft, and maybe one before or during training camp. Then handle it as events warrant. At some point you're just reworking the same basic material, so try to keep the features current and relevant. You also don't want to run three stories a week on the guy if they're a backup running back playing as a gunner on special teams.
Thinking back with our star player, we had a couple of bylined stories on him when he was a non-descript rookie trying to break into the lineup; a ton when he finally did something noteworthy; and then have averaged one or two a year since then. He does a youth football camp here every July, so that's an easy time for us to work a couple of different preseason story angles on him.
Once the season starts, adding their team's AP gamers to your coverage isn't a bad idea. Try to splice in their stats if they're not mentioned, no matter how mundane they are. If there's a photo of them, use it. Scour the press conference transcripts (and even other papers, as long as you give proper attribution) for extra quotes you can add to the AP story.
During the week keep an eye out for any news, stories and photos on the AP wire. There might be preview stories he's quoted in or notebook items that you can play up a bit, like if your guy plays cornerback and there's a story about the secondary or defense.
I'd also suggest reaching out to their NFL team's PR department for a photo or two when you do a feature. Most teams are happy to send you a couple, and then you can stash away the ones you don't use for future stories. Same with any AP photos you might come across, if your paper has a good subscription plan.
One thing I will say about NFL PR departments is that they are, by and large, very accessible and accommodating -- surprisingly so, really. Whenever we've had to reach out to do a feature on our local players we've never had much of a problem going through them to set up phone interviews even though we're nowhere near most of their markets. Our star player was on a team on the other side of the country and they always gave us the time of day or, the one time it just wasn't logistically possible to set something up, sent us some transcripts and such to help get the job done. So don't be afraid to reach out to them from time to time if you need something on your guys.