Can I pause a download and shut down Steam, then turn off my computer then continue the download the next day without having to start over again?
You can safely close Steam & shut down your computer in the middle of the download. You can continue it next time you use Steam (or if you want to use Steam but not download, you can do that too – just restart the download whenever you're ready).
For reference, you can also continue downloading whilst playing another game – details can be found here: How do I continue downloading a game in Steam while playing?
You can close Steam and/or restart your computer at any time while downloading with Steam. You do not need to manually pause the download before closing Steam or rebooting; the download is paused automatically and resumed next time you start Steam.
Unless you delete the game (either mid-download or after downloading) by right clicking the game in your Library and clicking Delete Local Content... then you will not need to restart the download.