oscillator design question

I'm trying to design a circuit that's supposed to self-oscillate. I'm a little rusty in analog design, but I've got the TI Op Amp chapter on oscillators and the reference books. I'm also simulating the thing in LTSpice.

So: I have what's basically an amplifier with gain A. When I apply an input test signal to the amplifier and look at the the output of the feedback β before closing the feedback loop, where it would be attached to the input feedback point (after removal of the input test signal) what should I see?

I know that when the loop is closed, the total Aβ should = -1; that is, the phase shift should be 180 degrees. However, in order to get this circuit to work I have to apply a phase shifter to get the right phase at the feedback, but making it 180 degrees (before closing the loop) doesn't seem to work. Other variants of the circuit that do oscillate seem to have a 90 degree phase shift before closing the loop, but I haven't found any literature that approaches the problem from this point of view.

Any suggestions would be appreciated.

An oscillator needs positive feedback. If it has only negative feedback then it is an amplifier, not an oscillator.
The phase shift circuit in an oscillator has a certain amount of signal loss which must be made up by the gain of the circuit.

A simulator does not know that noise is amplified and gets an oscillator to start oscillating. Then you must give an oscillator a KICK in a simulation to get it to start oscillating.

The oscillation condition (given by Barkhausen in the 1930th) requires a loop gain (gain of the open loop) of "1".
That means: If the passive frequency-determining circuitry produces -180 deg at the desired frequency, you need an inverting amplifier for closing the loop.
However, there other passive circuits (Wien band pass) with 0 deg. at the center frequency; in this case the amplifier must be non-inverting.

Please note that the Barkhausen's criterion is a necessary condition for oscillation but not a sufficient condition: some circuits satisfy the criterion but do not oscillate

https://en.wikipedia.org/wiki/Barkhausen_stability_criterion