I live in an apartment, an outdoor antenna or dish isn't an option. We have 3 options where I live: Charter, AT&T U-Verse, and cutting the cord. We're sick of paying $200/month and still not getting everything we want with cable and I refuse to do business with AT&T so we're kinda stuck.
I've read good and bad things about Sling so for but am still researching our options.
I've been a cordcutter for some time now and love it. The trick in my opinion is to not be married to one device/service. Different ones can be better for different things and different people. Here is my rundown of what I think might be a good idea for you to look at.
Devices:
The apple tvs are nice, but people are still behind on putting apps on their device. Over time, I might decide to jump back to the Apple TV, but right now the companies are a little behind with putting their services on the Apple TV so I suggest people to go a different direction.
The fire tv box (not stick) is a quality box that can do pretty much everything you would want, but for obvious reasons it pushes Amazon content. If you are a heavy Amazon prime user then you may favor that device. If not then I would pick the third option.
I personally like the Roku. If you have a 4K TV, a higher end internet connection and are interested in paying extra for movies and on a Netflix subscription, then the latest Roku is a great option. If you don't know what any of that is or don't really care, you can still get the latest Roku, but the Roku 3 is still a quality device which will meet all of your needs for several years.
There are many other devices, but if you are new to the streaming/cord cutting world then you will likely not be taking advantage of any of their more advanced features. Therefore my suggestion is to buy a Roku 3 and a hdmi cable for connection to the tv. That is all the hardware you will need except for an antenna which we will mention later.
As far as services. There are currently three options for getting sports channels as a cord cutter. Sling, PlayStaion Vue (psvue), and sfntv. Others will be coming soon, but these are the only one available now. All are available on the Roku and I believe on the fire tv. Only sling is available on the Apple TV.
I have used all three services so I will try to quickly give an overview of each.
I never had problems with sling, but I know people who did have trouble with lagging and buffering. This is annoying when watching anything, but it is an absolute deal-breaker for sports. In addition to that, the college team I follow is in the big12 which has a contract with fox and their fs1 and fs2 channels to show all of the football games. They also have a contract with ESPN to show all of the basketball games. You can get all of those channels with sling, but the cost is high compared to the other two services. For this reason more than any, I am not subscribed to sling any more.
Sfntv is a new service. First of all, I think there is some serious potential with this service, but it is only a month old so there are still some problems. It is relatively simple and straightforward to use and opporate which is a plus (though it is pretty ugly as an interface). They have done a lot of changing on their packages which is very frustrating. They were originally offering a straight sports package which included all the epsn channels and fox channels for $20. That is by far the best offer available for just sports, but that package is not currently available and I haven't found out how soon or if it will return. They do have other options available which include several channels. The picture quality is excellent with sfntv.
PsVue is the service I am currently sticking with. In my opinions, they have the highest picture quality (though sfntv is virtually identical) of any tv service, Internet based or otherwise, I've seen excluding directv. They also offer a solid group of channels including all ESPN channels, all fox channels, big ten network and some additional sport specific channels. They have three different tiers, but I like the $35 tier with all of the channels I mentioned above.
You have already gotten good advice on the antenna, but check the site and see what channels are available to you. It will show you where they are broadcast from and how far away they are. You can then look through their recommendations for an appropriate indoor antenna. They have gotten significantly better recently in look and quality. The site that was posted above will give you all the information you need about an OTA antenna so you can pick up local channels for nfl games.
I hope all of this information is helpful and not overwhelming. If you have any more questions then please post them and we can give more information.