Which type of oscillator should I use?
There are a lot of options, but here are a couple of examples:



The first (which is really a pulse generator), from Unijunction Transistor, shows that there are three outputs that can be taken: VC1 (sawtooth), VB1 (positive pulse) and VB2 (negative pulse):



$$T = \frac{1}{f}= R_3Cln\left(\frac{1}{1-\eta}\right)$$

For a 2N2646 Unijunction Transistor, the intrinsic stand-off ratio η as 0.65, as stated in the data sheet.



An example of an astable multivibrator using emitter-coupled oscillators can be found in Electronics Tutorials - Astable Multivibrator



The periodic time is given by:

$$T = t_1 + t_2$$

$$t_1 = 0.69R_3C_1$$
$$t_2 = 0.69R_2C_2$$

If 

$$R_2 = R_3$$

and 

$$C_1 = C_2$$ 

then the frequency of the resultant symmetric waveform is given by:

$$f= \frac{1}{T} = \frac{1}{1.38RC}$$



I, myself, looked into the subject of oscillators recently, and I found some which used only discrete components and came up with a number of options, which I listed in my blog, Swingers.