In the end "best" is judgmental. There are two options:
- Install a fully functional local TeX system. For that the obvious candidates would be MiKTeX, MacTeX, or TeXlive, and in terms of ease of installation for most students either MiKTeX (Windows) or MacTeX (OSX). (Linux users would probably want TeXlive, and may need to be warned about the tendency for distribution packages to be considerably out of date.)
- Use a cloud-based system, of which the most commonly used is now Overleaf
Although there are pros and cons to all these choices, there is a lot to be said for beginners in using a cloud-based approach in terms of your criteria. It offers a straightforward LaTeX compiler and editor, with nothing to install, and it works pretty intuitively. It's free for personal use. It's "real LaTeX" and mostly any document that compiles there will compile on other systems in the same way. There are good reasons for experienced users to prefer to maintain a local system and their are occasional disadvantages to being in the cloud: but as a way to get going quickly without installing anything, it may have much to say for it.
To my mind the main practical downsides are (1) occasionally the cloud-based systems lag behind bleeding edge TeX development (but that is unlikely to be a problem for most users) and (2) Overleaf seems to encourage the use of non-standard "templates", some of which are of dubious quality or utility, and which may not be portable. But (1) is unlikely to bite new users, mostly, and (2) can be avoided by encouraging people to use Standard templates.
There are obviously more principled reasons why people might refuse to use cloud-based systems and circumstances (e.g. confidentiality concerns) in which they would not be appropriate. But if your students are not handling sensitive personal data, or commercial or government secrets, and do not have rooted objections to the use of anything in the cloud, those do not seem to be deal killers. Some might have other personal views (for instance preferring to use a particular editor).
In the long run, if someone is going to use LaTeX a lot, there are very sound reasons to move away from such systems to something more controllable. At that point the sort of information provided at the LaTeX project page and by TUG is useful.
Arguably as important (and here again the cloud based systems tend to help) is encouraging users to use modern practices (such as UTF encoding) and packages from the start.