I want my own bash environment vim tmux and so on, that I can customize for my develompment needs. Then upload it to github and install whenever I set up my computer new. Any HowTo's how to proceed?
All of the command line utilities you mention (bash, tmux, vim), and many others, run a dotfile in your home directory as part of their start-up sequence. Traditionally, these dotfiles were called after the name of the command with
If you want to persist your settings for any of these tools, put them in the rc-file. For instance, to enable syntax highlighting in vim, add
Dotfiles are part of Unix lore and if you search the internet you'll find the most elaborate examples of things you can do with them. There actually is a place on Github for dotfile fanatics to share their inventions with others: Github does dotfiles. Happy dotfiling.
Now that's an open ended question.
You don't need to "install" your own bash, but merely customize bash to your needs. Well, assuming bash is installed... but it should be :-)
Bash implicitly support per-user customization though various resource files it reads on startup: ~/.bash_profile, ~/.bash_login, and ~/.profile, as well as some global files as well.
Familiarize yourself with bash's startup procedure here: Bash Reference Startup files. This will tell you where to put what so that your bash environment behaves they way you expect (especially the differences between interactive, login and non-interactive/non-login shells which can trip up anyone).
Then, The Bash Hackers Wiki seems like a good source for learning about everything else concerning bash.
There are others as well: The Korn shell (tsh), T-shell (tcsh) and others.