make a testfile and run it with:
mkjobtexmf --jobname <file> --cmd-tex <latex>
<file> is your source file <latex> is your LaTeX command, e.g. pdflatex or simply latex.
The Perl program mkjobtexmf creates a directory <file>.mjt which is a compatible texmf directory with all loaded files of your example.
If you are running windows then you'll need an installed Perl, e.g. from
http://www.activestate.com/perl/
However, I never used it under Windows, with Linux it is very useful.
How do I decipher these headers?
This is pdfTeX,
It's PDFTeX, an extension to Knuth's original TeX system to produce PDF output rather than DVI (along with some other extensions)
Version 3.1415926
Every few (or not so few) years Knuth addresses accumulated bugs and revises TeX, adding another digit. These bugs are harder and harder to find and if you have any TeX from around 3.14 (last century sometime) there's unlikely to be any differences in output unless you write a test document specifically to show the bug that was fixed.
-1.40.11
This is the pdftex version number. There was a period when pdftex was more experimental and likely to change than classic TeX ,but now it's pretty stable (not least because I think Hàn Thế Thành is looking more to luatex these days).
(TeX Live 2010/Arch Linux)
So you have that TL build
(format=pdflatex 2011.4.11)
and a format using latex that was built on that date (the date the format was dumped, not the date of the latex format). Latex format (unlike latex packages) is very stable (the new 2014 release is identical to the 2011 one apart from the date, for example).
If you get different results from the same document on two machines, don't look to these headers, add
\listfiles
to the preamble and then look at the list of packages and version numbers that appears in the log. Differences in package versions are almost always the cause.
Best Answer
As the comments indicate, it would help to know the operating system, but the answer for TeXlive (which is cross-platform), installed via the net installer, would be the "Basic Scheme" (See here for a listing of schemes). There is also a scheme called "minimal", but I think this would only give you support for plain TeX, not LaTeX.
If you're on linux, however, you might be more interested in what package distributed through your distro's repos is smallest. But then we need to know which distro. On mac, you might prefer the BasicTeX version of MacTeX, though this is by no means completely minimal. On Windows you might install the Basic MikTeX, and then not install any additional packages. (I don't think this is completely minimal either: if you really want minimal, TeXlive is probably your best bet anyway.)
Licensing conditions are not much of a factor here. All the basic stuff would be covered under the LPPL; it's only if you went beyond that there would be any issues.