Re: Will starting a new game make me lose my current saved game?

You can have many save games: http://sims4.crinrict.com/en/2014/09/save-games/ 
Click in the start screen on the little + button you see in the first picture. It might be handy to name your current save a good name so you know what is what.

And to make sure you never lose any of your games, make a backup: http://sims4.crinrict.com/en/2014/09/backups/