Here is what I would do (step one)
Get the data sheet for the LTC6900. It is a good resistance to frequency oscillator.
You will need a good source of 5 volts or 3.3 volts. (LM7805)
R1 needs to be a fixed resistor and a pot. (you can do that)
The output is o to 5 volts, but I (you) can fix that later.
One IC, very small.
View attachment 96533
If I built this I would put a three way switch on "DIV" pin, and make a 1khz to 1mhz project. It would be much more useful.