As a brief answer to your question:
- MikTeX is absolutely free, and the majority of it is free as in speech.
- It is a straightforward installation and should be relatively familiar to you if you've installed programs before. Normally you need administrator privileges to install MikTeX, but there is a portable version available which has no such restriction, and can even be installed on a flash drive.
- LaTeX itself is not strictly stand-alone, but everything you need is included in MikTeX.
- MikTeX is one of the more popular distributions of TeX for Windows, but others exist (see below). Usually, it doesn't matter what distribution you use;
TeX is TeX wherever you get it.
- We on TeX.SX collectively use many different variations on Donald Knuth's original TeX, although many of us stick to the one that we prefer instead of switching back and forth.
Preamble: What exactly is LaTeX/MikTeX?
Using LaTeX means you write some text combined with some strange command structure. This can be done either in Notepad or your favorite editor <Censored to repel nerds> and that would be basically your .tex file.
Then you feed this file into a TeX compiler and TeX starts to understand what you mean via interpreting the commands in the .tex file. There are a couple of options for the end product; some produce a .ps file some directly a .pdf file (or .dvi but let's forget about that for a second)
Now MikTeX is the collection of packages and the engines that receives your .tex file and produces some output. On Windows it's kind of the common choice. TeXLive and MacTeX are other major distributions for different operating systems; TeX Live is cross-platform, where MacTeX is for OSX.
Also there are some editors that allows you to type .tex files and when you press a button, or if you feel hip, a shortcut the editor sends your file to MikTeX for compilation automatically. The most popular choices (for Windows) are TeXnicCenter, WinEdt, TeXworks, etc. See LaTeX Editors/IDEs for more options.
What is a TeX distribution?
Regarding MikTeX, first and foremost, it (and almost all software having to do directly with LaTeX) is absolutely free - it is open-source. It is very unlikely that you will have to restore your computer after installing MikTeX - almost as unlikely as having to restore it after downloading a paper. Just be sure to follow all your normal installation dos and don'ts: try not to let the power die while you're installing it.
More technically, MikTeX is what is called a TeX distribution - it is a bundle of programs and files that are commonly used when working with TeX and its many derivatives, of which LaTeX is the most popular. MikTeX includes, among many other things, the actual latex program. It is a standalone piece of software that you can use either from command line or from a graphical interface such as TeXWorks (which is also included in MikTeX).
So with MikTeX, you get
- An editor made specifically for editing LaTeX source files (TeXworks),
latex (+friends) to actually process your document into something share-able,- Yap, which is to
.dvi files as your favorite PDF viewer is to, well, PDF files,
- A fairly good GUI for a package manager, which helps you download packages (plugins, essentially) written in LaTeX for LaTeX (for the most part), and
- A settings manager for the nerds.
A TeX distribution is thus designed to be a complete 'starter kit' for working with TeX, but there are differences between different TeX distributions. For example, MikTeX is somewhat easier to set up than TeX Live, another distribution mentioned in the comments. However, choosing MikTeX comes with a few obscure security issues, as described in What are the advantages of TeX Live over MiKTeX?, but you are unlikely to come across these (and almost sure to never come across them if you're using it for yourself). Installing and working with TeXLive is a separate topic, but more information can be found on TeX Live's webpage.
Learning More
As far as learning LaTeX itself, there are countless resources available for free on the internet. Among the highly recommended are
Of course, there are excellent printed-and-bound guides and manuals available as well, including
Since you're new to this site, I would recommend checking out the About page and The Unofficial TeX-SX FAQ; these will give you a far better introduction to TeX.SX. Of course, if you have any more questions, don't hesitate to ask (but do be sure to use the search feature first!).
Good luck!
