Regarding M-x eshell:
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Eshell is not a stand-alone shell; it’s implemented in pure elisp, so can’t be run outside emacs, which is why it’s not one of the standard shells. It doesn’t have its own scripting language like bash/zsh/etc. have; it has elisp, and some command interpretation stuff to make calling elisp a little cleaner.
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I can’t speak to zsh vs eshell, but I’ve mostly switched from bash to eshell. 95% of the time, eshell does everything I want or need without any problems. I don’t use it for ssh. Also, you can’t background a process once it’s started (but you can start it backgrounded).
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It’s going to be really hard, because zsh has a full scripting language, whereas eshell is basically an interface to the elisp interpreter. What are you looking for in an interactive shell? Eshell can probably do most of it. Conditional statements and loops on the command line? Sure. Aliases, functions, wildcards, programmable completion? Sure.
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The way I migrated was to basically start from scratch. Every time I ran into something that I didn’t like or I wished it did, I’d figure out how to get it to do what I want. For example, eshell uses pcomplete.el for programmable completion, so adding completion functions is pretty easy.
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Integration with emacs is the big win for me. You can have elisp functions piped to shell commands. For a silly example, try:
message "hello world" | cut -f 1 -d ' 'Some commands (notably grep) get put in emacs buffers, so e.g. you can quickly jump to the results.
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Depends on how much time you really spend in emacs. If you do everything in emacs, it’s useful, because sometimes it’s easier to pipe together elisp commands with other commands through eshell. If you don’t find yourself copy&pasting between emacs and your shell too frequently, it’s probably not going to be a win, and you’re going to have to spend time customizing it to the point you’re comfortable with it.
As an alternative to eshell, M-x shell runs your normal shell underneath which interprets all the commands (so doesn’t have access to elisp functions), while command-line editing (and therefore programmable completion, history, etc.) is done by emacs. I use it for ssh.
One other alternative is M-x term, which is a terminal emulator inside emacs, and usually runs a shell underneath, and the shell does all of its normal things. Then there’s absolutely no conversion/adaptation steps required.