The width tool and width profiles are good if you're simply adjusting the width...
If you want more control over the appearance, another option is to use art brushes. Simply draw your brush (as a straight line) and drag it to the Brushes panel, selecting "Art Brush" from the "New Brush" dialog[1].

You then simply set the path to use that brush...

You can save brush libraries to use again and again so they're pretty useful (you can find a bunch of free ready-made brushes on the internet if you don't want to make your own too).
[1]
You'll likely be OK with the default settings but you can control things like the colorization method (so you can change the brush's color just by changing the object's stroke color), scaling methods (so you can stretch/scale certain portions of the brush) or change the orientation...
Art brushes will stretch the entire brush over the length of the path. If you want in to repeat over the path then you can use a pattern brush or scatter brush instead (where a pattern brush simply repeats, and a scatter brush can create more complex and random arrangements).