Hey Buck. I think the truth is that most guys get lost, thinking they need tons of shirts, and end up with overly full closets that are lacking in consistency in features or patterns or colors. Most of them would be better off with just 5-10 really great shirts that party well together and look good no matter the season. So yours is a really good question.
So I know you asked specifically about sport shirts, but we like to think of our dress shirts as "weekend sport shirts," because they can easily play for both teams. (Remove jacket, remove tie, roll sleeves.) So you'll see a little overlap here. All of these have a modified spread collar with a slight roll, thick Trocas shell buttons, and German interlinings (lightly top-fused for dress shirts, non-fused for sport shirts) that make up the gold standard for us. With basketball season starting to hit its stride (maybe) - here are my "starting five" shirts:
White Poplin (the one to dress up, or not): Everyone needs an elegant white shirt - one that can take you upstairs to the boardroom, or downstairs to the lobby bar. Of course we think our white poplin dress shirt is pretty close to perfect, and just might be the most versatile shirt we make. Don't let the "dress" part fool you... this one looks just as incredible with a pair of old jeans and the sleeves rolled up, as it does under a navy suit. A shirt for all seasons and all occasions.
Sky Rox aka Sky Royal Oxford (the one for 7 days a week): This might be the one shirt that literally every SM employee across the company has in his closet. It's the universal building block, and who doesn't a love a shirt that matches the color of the summer sky? Royal oxford (we call it roxford) is just a touch more refined, and a little lighter than, a traditional oxford... partially because it's actually a completely different weave. But it can also go casual, especially when you get a couple of washes in. I don't think I've found anyone who doesn't look great in it.
Bengal Stripe (the one with a non-pattern pattern): I don't want a closet filled only with solids, and vertical stripes are an easy way to mix it up... but in a subtle way. Think of it as an intro to patterns. This small Bengal stripe is a bit sporty, and goes with almost anything (jeans, chinos, shorts, blazer, no blazer). We like the idea that you should be able to get dressed in the dark, and this one comes with the exact same benefit.
Chambray (the one for the weekend): We love love love chambray and this one's our go-to: an incredible, lightweight, slightly crispy Italian chambray made with linen and real indigo. There's just a comfort and naturalness to it. It's been one of our favorite sport shirt fabrics since day one, which probably explains why we found so many different ways to use it! You'll see various riffs in spread collar sport shirts, band collar shirts, western shirts, slim fit shirts, handmade "Otto" dress shirts... and Ann has a few in her store, too. So yeah, we like chambray, and think you'll find some utility in it, too.
Graph Check (the one for the "second look"): This is as traditional as it is easy to wear. We like the idea of a suuupppppeeerrrr subtle pattern, because from a distance it reads as a solid. Another non-pattern-pattern/NPP. The details don't scream at you but rather quietly reveal themselves... hence the "second look". This thing only gets cooler when you pair it with jeans or 5-pockets, or even under a solid sweater in the chilly season. And not to sound like a broken record – YES, a graph check will look great under a blazer or with a suit, too.
BONUS! The 6th Man Award Goes To... A Fun Shirt: Versatility and building blocks are clearly key attributes to my starting five. But a good 6th man (aka, a guy who often brings a spark or energy off the bench) can be a key ingredient for a basketball team's success. To put it in shirting terms, everyone can use a shirt that's a little different and just makes him feel cool. Lately my go-to is a brightly colored awning stripe - I like how unexpected they are in a color other than blue. Of course, every guy is different, and a 6th man shirt can lean more traditional, like a button-down in a quiet tartan, or a little louder, like a psyched-out Liberty of London print or a super-bright color. We've got a TON of interesting ones in our semiannual sale, which might be a good, low-stakes place to start looking.
Anyway, Buck, hope this helps. In the end, I think sport shirts are just like anything else: dial in your fundamentals first, then start having fun and getting creative with it, and see where that takes you. Enjoy!