In all cases you only need the (partial) runtime to run, not the SDK. The SDK is only for development.
As for the rest:
- on some operating systems a .net version is available by default. These versions can change beteen OS (Windows) versions. You'll need to see which version is applicable for you.
- .net core (and it's follow up .net 5+) is not always standard available on the OSses. But .net core (and .net 5+) offers the ability to include the required runtime components in the build. This will increase your build by approx. 140 MB, but you can be sure you have all the required prerequisites.
You can pick whatever suits you best but be aware of the end-of-life-dates of the framework: .net, .net core, .net 6+.
For version 4.5.2 specific:
.NET Framework 4.5.2, 4.6, and 4.61 retire on April 26, 2022.
So I wouldn't start developing new applications with that version.
As mentioned by @MAtthewWatson, more info on the single file publishing (which includes the runtime), see: this link.
Captured image in case the link will change:

