There's two general flows to get good content after you cut the cord:
1. content provider via set-connected device → TV screen
2. computer screen → set-connected device → TV screen
Start with 1. Content providers can be things like Hulu and Netflix that let you browse a library of titles for a subscription, or iTunes or Amazon which let you buy or rent individual titles. Set-connected devices are things like AppleTV, Roku, Fire TV (Amazon) and Chromecast. Gaming rigs like Xbox / PS4 fit here as well. Not every provider is available on every device; if you already do a lot of purchasing in the Apple ecosystem, for instance, or you own a lot of Apple hardware, get the Apple TV and not a Roku. If you use Android / Google Play to get media a lot, a Chromecast or Roku is probably better. If you use Amazon Prime a lot, you might consider the Fire TV. If you see gaming being a component to your entertainment, pick an Xbox or Playstation. I'd say Roku is the safest "agnostic" choice if you don't already line up in a content ecosystem. Hulu, Netflix and free stuff like Youtube and are available on everything. Also, if you have a buddy/relative that maintains a cable account, it's not unheard of to share passwords and log in to WatchESPN (crucial for live sports, hardest to come by for cord cutters) and maybe even HBO Go. Those services are, as of now, still tied to having cable accounts even though you can get them via streaming.
Then, 2. Wirelessly streaming a computer screen to your TV is a key component to the cord-cutting experience in my opinion. It helps you "fill in the cracks" and watch things you can't find via the device you buy. So you can stream stuff from websites (all the major networks put shows on the web that don't always show up on the streaming services), live sports streaming over the web, or maybe that movie or TV show you may have have as a file. If you have Apple hardware, Apple TV makes this easy. If you use a PC, get a Chromecast and you can stream anything to it from the Chrome browser. I honestly don't know what the other boxes let you do, or what third-party software you might need; I use Apple for everything and it really does just work.
That's where I'd start.