I recommend reading a book on analog analysis/design.
If the collector emitter voltage (Vce) is about 0.3V across a silicone diode, and I have a voltage divider between 33Ohm and 100Ohm, should I be expecting a ~2Vpk-pk?
You cannot assume \( V_{CE} = 0.3\, V \). Look up regions of operation for the BJT. In the forward active region, \( V_{CE}\) can vary quite a bit while maintaining relatively constant \(I_C\). The only thing you can assume is that, when the transistor is on, you have about a 0.6V drop across the base-emitter junction (or across the emitter-base junction in the case of a PNP BJT).
To figure out why you have a 1V drop from emitter to ground, analyze your circuit. Using Ohm's law when the input is high, we can derive a set of equations and then solve:
\[ V_B = V_E + 0.6,\]
\[ 3 - V_C = 33 \cdot I_C,\]
\[ V_E = 100 \cdot I_C,\]
\[ 3 - V_B = 47000 ( I_C/\beta) = 47000 (I_C/300).\]
I get \(I_C = 9.4\,mA\), \(V_C = 2.7\,V\), and \(V_E = 0.94\,V\). The emitter voltage lines up with what you have which is about \(1\,V_{pp}\).
If you wanted \(I_C = 15\,mA\), you could divide that by \(\beta\) (to get the base current you need) and also solve for emitter voltage and then add \(0.6V\) to get \(V_B\). Then do Ohm's law to find required base resistor.
Usually when biasing BJTs, I think about what signal swing range I need and bias accordingly. Textbooks talk about biasing schemes such as biasing so that \(V_E = 1/3 V_{CC}\) and \(V_{CE} = 1/3 V_{CC}\) and so on.
Also, it should be noted I've approximated \(I_C \approx I_E\). You can be more exact with your analysis although I suspect variance in beta will probably throw off calculations from reality more than exact \(I_E\).