Chances are good that if the old chain elongated a bunch, a new chain will skip on your old freewheel. So, don't be surprised if you need a new one of each. Chainrings tend not to skip unless they've really been abused.

If you want to upgrade to 5800, you won't get any argument from me, but if it were my bike I'd probably just keep it C&V and replace drivetrain parts as necessary: chain, freewheel, chainrings, etc...