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I like the simple auto completion provided by Ctrl-N but not typing Ctrl-N everytime to get the completion.
I would like it to work similar to how YouCompleteMe works with automatic suggestions. If possible, I would also like to cycle through the completion menu with Tab without losing the functionality to indent.
Take a look at the vim-autocomplpop plug-in, which triggers the completion menu automatically as you type.
For using "Tab" instead of Ctrl+N in the completion menu, you can use a simple mapping such as:
inoremap <expr> <Tab> pumvisible() ? "\<C-n>" : "\<Tab>"
As an alternative, you might want to consider the SuperTab plug-in. It doesn't really do "as-you-type" completion and requires you to use the "Tab" key to initiate completion, but it's quite powerful and it has nice features you might like. (Note that I wouldn't expect SuperTab to work well with autocomplpop, so you might be able to pick one or the other, unlikely to be able to pick both.)
You can get completions as you type with MUconplete. For me the advantage over similar plugins is that it is lightweight, doesn’t have dependencies (is pure Vim script) and although it only cares about Vim native sources it works quite well if you hook an LSP to omnifunc.
To manually trigger the menu, MUcomplete maps Tab, but you can override that. I never use them. Once the menu is open you can navigate with Tab and Shift+Tab without problems
