In the second schematic, a 555 circuit drives a comparator circuit. Within some limits, the two halves are pretty much independent of each other, so you can change one side and keep the other. The 555 datasheet has minimum and maximum recommended values for the timing resistors. The minimum value would be the fixed resistor, and the maximum value would be the variable resistor. In the post #8 schematic, the two resistors are in series, so it doesn't matter which one comes first.
Not that a single range will not be very usable. At the higher frequencies, a small adjustment of the pot will cause a large change in output frequency. That is why the second schematic has C1 through C4. For the same R1 and VR1, each capacitor creates a different range of output frequencies. The equation to calculate the output frequency is in the datasheet.
The LM2903 has the same number of pins as the LM393. Both are dual comparators - two independent comparator circuits in one package. For both parts, if you are using only one comparator then the inputs to the unused circuit must be connected to something, not left floating. Connecting one to V+ and one to GND is safe. It doesn't matter which goes where.
How are you going to assemble the circuit (perf board, solderless proto-board, etc.)? You should consider getting a small function generator or PWM circuit kit as a starting point.
ak