Work backwards !! What do you want to achieve FIRST ! ie Freq range, duty cycle, levels, rate, sweep?, min, max etc etc THEN you can plan on HOW to do it.
You'll find that once you set your goal, options like using a simple 555 may be totally unusable, you may even need to go to a simple micro.
In days gone past, I've made up several Functions generators eg, some based on the "latest" function generator ICs (back then), and some on building
blocks of linear / digital modules, then finally to a micro. 101 ways to skin a cat :-)