The "which version should I use" question is easy too: the latest release in Long-term support branch, which at the time of writing is the 4.2 one.
Another benefit is that Node 4 bundles npm v2, which is more mature than v1 bundled previously and significantly faster than npm v3, which comes with Node.js 5.1. For instance, on one of our machines, installing the CLI itself took 80 seconds less with Node 4 against Node 5.
Let's not forget that Node.js 4 works better with Windows 8 and 10, if this is your workstation of choice.
Being a LTS means that it receives first all the critical security fixes, which is important for software which is exposed to Internet.
Even Node.js maintainers state that "The Node.js core team will continue to ensure that v0.12 remains a viable platform for production deployment until the end of 2016. However, users of v0.12 should be working on plan to migrate to at least v4 LTS (Argon) as soon as practical."
To answer the last question ("how long a given version is supported"), we monitor the current share of the different Node.js versions. When one drops very low (in the single digits), we consider stopping testing against it, and thus our support. We warn about this at least one release in advance and, according the feedback we get, may extend its support.
To sum up, if you are using another version, we urge you to try Node.js 4.2 now!
The NativeScript team