I have a Twitter account based on Basketball news and updates, and I'm not necessarily trying to make money from it, but rather I'm trying to gain legitimate followers. Why am I doing this? Because I love talking about Basketball (NBA/NCAA). My competitors are Bleacher Report, SLAM, theScore, SportsCenter, ESPN, etc.
How can I standout from my competitors? I guess I could do giveaways on products, that would help me gain a following I'm sure, but at a certain point that probably wouldn't be a sustainable practice as I would need funds to continue doing that, and once the giveaways stop, no one is going to care about my page anymore.
I've been thinking hard on this one and I'm just not sure. Maybe I could create my own media and post it (i.e memes, compilation videos, images, etc.), but my competitors are already doing these things. Any suggestions?
Really good question. About 15 years ago, you had the major sports sites--ESPN, Yahoo! Sports, Rivals, etc. Then individual sports fans learned that they could start their owns sites and create content that was different than the "buttoned up" / corporate sites. People Bill Simmons got started on an AOL site, and Will Leitch was given the green light to start Deadspin for Gawker Media. That gave the non-corporate / "true fan's" take an it was very successful. Before long, there were tons of these blogs out there started on Blogger and most didn't amount to anything.
Simultaneously, enterprising beat writers would start blogs that covered specific teams or specific topics from a niche. If you were a hard-core Washington Redskins fan, someone like Dan Stienberg would keep a blog that was solely dedicated to your team. From my telling, social media act as appendages for their individual websites.
Here are my recommendations:
Sports writing is a very popular niche. Almost every guy likes sports to some degree and the idea of covering sports for a living is very attractive. Thus is a very saturated niche and it will be hard to break out. The effort you put in, even if you do break out, might not pay more than a minimum wage job. Meaning that the upside potential isn't all that great. Honestly, you should find something else to do.

It could take YEARS before getting a following and that time would be spent doing something else.
But if you persist on this path, you need to differentiate yourself and you need to find a successful niche. And offer really smart / specific coverage on a topic that can gather a wide enough audience. Cover the sports from a different perspective. I'll give you two names:
1. Mike Axisa kept a blog called River Ave Blues which is a stat / news focused blog of the NY Yankees. He's also got a twitter / facebook / instagram account. He obsessively covered the Yankees for like 10 years until he closed the site recently. Now he had a full-time writing job for CBS Sports and has a Yankees Patreon account which brings in (last I checked) $30K / year on top of the job. That's some nice dough, but it took a TON of work.
2. Rob Friedman AKA the pitching ninja. His social media account of baseball pitching gifs and methods built him a following and now he does work for ESPN, among others. But he had really smart intelligent takes on really small niches.
Maybe you can write a smart-mans basketball blog with cool gifs / pics and tips on how to play the game better? Maybe why some obscure player that people haven't heard of is better than expected? That kind of coverage. It might get you years to get noticed and build up a following, but if it's really your passion, I think this is the only way to succeed.
Good luck. I don't envy you.