How to design an Oscillator Circuit (500 MHz range) with no Op amps?
I'd use a colpitts oscillator. In fact i've just been designing one at 250MHz. Here's the general design: -

The diagram shows a 50MHz oscillator but if you use a high-speed transistor that has an Ft of 5GHz or above you'll get decent results at 500MHz. If you want it to work at 3V3 make R3 = 2k2 and R1 = 1k. I'm trying to remember the transistor I used - it was from NXP - it'll come to me later..... BFR42A!!
JFET colpitts (even simpler): -

The JFET to try is a BF545B. It should work at 3V3 but don't load it too much. The cap on the gate would be about 4p7 and the cap across the source resistor would be about 10pF. Inductor about 12nH. You need a JFET with V(th) less than 3V for it to oscillate. The output was through a 2pF to a common emitter circuit using a BFR42A. If you are lightly loading it you'll get away without the 2nd stage. The sinewave purity was very good but still would need another 20dB of attenuation at the 2nd harmonic for it to be reasonably pure. The source resistor was about 1k5 but this depends lot on the jfet you choose. It's always amazed me how much simpler these circuits are compared to BJT's - no bias resistors - the JFET biases itself thrugh the voltage developed across the source resistor and the fact that the inductor keeps the gate at 0V. Anyone remember valves?
Both designs can be tuned with a varactor diode and that can also be used for FM data modulation. To keep it in tune I have used an ADF4111 around it. It's a PLL and needs a couple of registers setting up with a PIC or similar.