@ShawnS: Welcome to ElectronicsPoint! We DO cater to newbies here, so feel free to ask lots of questions. The better you can describe what you want to DO, the better the advice you will receive. A lot of folks come here with some idea of how they want to DO something, but if they are inexperienced their idea may be impractical. Your idea of using an RC oscillator, either a phase-shift version or a relaxation version, is very practical. But as you may have noticed, depending on the circuit and component values, it can be subject to unwanted frequency drift. I will describe an approach that is not susceptible to such problems.
If your design goal is to have the RTD produce a stable square-wave frequency (< 10kHz) that is a function of its resistance, then I would suggest that you use a PIC microprocessor to (1) generate appropriate frequencies at one of the PIC output ports and (2) measure the RTD resistance using the PIC's built-in 10-bit analog-to-digital converter.
A simple look-up table translates the digitized RTD resistance values to frequency (or period) constants that are used by firmware you write to generate the output wave forms. The wave forms are rectangular in nature (square waves) since the output is from a digital port.
OTOH, if later you want something approximating a sine wave, say for purity of audio tone, that will require some extra effort. The extra effort could be as simple as a low-pass filter to remove the higher-order harmonics of the square-wave outputs. Considerably more complicated would be a digital-to-analog converter (not recommended or necessary, based on what you have revealed so far) driving an appropriate low-pass filter.
A possible disadvantage of the PIC approach is the discrete nature of the frequency increments as a function of temperature. Depending on your application, this may or may not be a serious problem. With the 10-bit A/D in a
PIC16F15325-I/P (for example) the RTD will be digitized to a resolution of one part in 1024 (0 to 1023), which is 2
10. That's a fair sized lookup table, and with 16-bit values for each table entry, a frequency resolution of one part in 65,536 (0 to 65,535), which is 2
16.
Some arithmetic on your part would be required to set the range of RTD resistance values that are digitized to fit into a 0 to 1023 "measurement range," and some more arithmetic and careful thought on how to use those 1024 digital values to address a lookup table stored in non-volatile program memory along with your program. Even more thought on what 16-bit values to place in those 1024 locations to achieve the frequency range you want your RTD to span as its resistance varies with temperature is required. This is perhaps the hardest part because the values will depend on the algorithm you decide to code to implement the square wave frequency output. If you can tolerate the coarseness of the frequency resolution, you could ditch the lookup table and use the digitized RTD resistance values as the input to your square wave generation algorithm. That does limit the frequency range to one of 1024 discrete frequencies, compared to one of 65,536 discrete frequencies with 16-bit lookup table entries.
Moving from an all-analog solution to a hybrid analog/digital PIC solution has some advantages. The number of components, required to implement a PIC design, is minimized. Most of the "design" is moved to the software/firmware domain, meaning it is much easier to troubleshoot (debug) than tweaking component values in the hope of finding the right recipe for success.
You could also implement a prototype hybrid analog/digital design using an Arduino platform, which eliminates the considerable amount of learning required to select and program a PIC, but at the expense of a much larger "footprint." Later, if so inclined, you can translate the Arduino design to a more compact PIC design.
Please let us know if a PIC-based or Arduino solution is attractive. There are folks here who can help you with either choice, plus
Microchip has a forum too.