Since I usually work with small laptop screens I tend to use vim tabs more than split. I find these key combinations quite comfortable:

nnoremap L :tabnext<CR>

nnoremap H :tabprevious<CR>

nnoremap <C-N> :tabnew<CR>

Also if you use offline docs (I only know Zeal) it would be pretty helpful to map the offline doc application to the K key depending on the language

nnoremap K :exec "!/usr/bin/zeal --query ".&ft.":".expand('<cword>')."&"

The above copies the word under the cursor and query it with zeal.