These days, just about any non-embedded (or large embedded) operating system has a POSIX:2001 a.k.a. Single Unix v3 compatibility layer. This is native on unix platforms (Linux, Mac OS X, Solaris, *BSD, etc.) and installable on other platforms such as Windows and Android. POSIX specifies a shell language, usually known as POSIX sh. This language is derived from the Bourne shell.

Most unix systems have one of two implementations of POSIX sh: ksh or bash, which have additional useful features compared to POSIX. However some less mainstream systems (especially embedded ones) may have only POSIX-mandated features.

Given your objectives, I see three choices:

• Restrict yourself to POSIX sh. Pro: you don't have to worry about differing variants, since there's a standard and compliant implementations are readily available. Con: you don't benefit from bash and ksh's extensions.
• Use the intersection of ksh and bash. This is attractive in appearance, but it does mean you have to use two reference documents instead of just one — and even the features that bash and ksh have in common don't always use the same syntax. Figuring out which one you want to use on a given system is also a pain.
• Choose one of ksh or bash. Both bash and ksh are available on all unix-like platforms and on Windows. Both have an open source implementation (the only one for bash, ATT ksh93 for ksh) that can be installed on most platforms. I'd go for bash over ksh for two reasons. First, it's the default on Linux, so you'll find more people who're used to it. Second, there are systems that come with an older, less-featured implementation of ksh; even if you can install ksh93, it's another thing you have to think about when deploying.

Forget about csh for scripting, and forget about zsh if you want common default availability.

See also What are the fundamental differences between the mainstream *NIX shells?, particularly the “for scripting” part of my answer.

Note that shell programming involves other utilities beyond the shell. POSIX specifies those other utilities. “Bash plus other POSIX utilities” is a reasonable choice, distinct from “POSIX utilities (including sh)”.

csh is almost always wrong.

Z shell (zsh)

It's said zsh is the most powerful for now so I would recommend trying it.

1. No matter which shell you learn - their syntax is very similar. Only built-in commands may slightly differ. But don't choose those old and unmaintained.
2. Bash is the most popular. But almost every command in bash works in zsh the same way. There are some exceptions of course.
3. AFAIK, every shell handles it the same way. But be warned - shells are stupid, they are not as smart as programming languages.
4. I saw zsh working on all Linuxes, FreeBSD and OpenSolaris.
5. See 4. Distros have zsh in their repos.

Why I prefer zsh (Z shell) to bash:

• files matching like this: for file in ./**/*.java; do ... (I mean ./**/*.ext)
• wants me to confirm when I do rm * :)
• tab-autocompletion is a lot better, I can write dmdomi[tab] and it suggests dnddomainname. java wants class name as the first parameter, zsh will suggest all classes available in the package and all subpackages.

But you are not limited to zsh only. If something does not work for you, you just write it in bash or sh. This is what is "#!/bin/bash" on top of the script for. :-)

To start quickly, use my .zshrc config: http://www.rozne.geozone.pl/.zshrc The only thing you should change there is export LANG="pl_PL.UTF-8". You probably don't want Polish locale.