79XX datasheets show differing capacitors on input and output. What is correct values and types to use?
Your situation needs caps for three purposes.


Hold up. Since you are using rectified AC, you need to hold up the voltage until the next sine wave. An approximation with margin is to assume that you need to hold up until the next peak. This is also referred to as bulk capacitance to keep the ripple to an acceptable level (as Tony described in his comments).


Allowable drop (ripple) = Vpeak - Vout - VdropOut

For your case, Vpeak = 18V, Vout = 12V, VdropOut = 1.3V (from spec)

Allowable drop (ripple) = 18V - 12V - 1.3V = 4.7V

Next calculate how much capacitance is needed.

C = Current_Draw * Hold_Up_Time / Vdrop

Current_Draw = 0.5 A (from your comment)

Hold_Up_Time = 1/120 = 8.33 mS, assuming full-wave at 60 Hz

Cap = 0.5A * 0.00833sec / 4.7V = 882 uF

If all the assumptions are correct, 1000 uF seems to be in the ballpark.

You need to be confirm that your peak voltage is really 18 Vdc after the rectifier (with a load). If you want it to work if the line is 10% low (recommended), then recalculate with 18V - 10%.  


Stability. Some regulators need a small cap with low ESR (equivalent series resistance) near the input and/or output for stability. Others may not absolutely need a cap, but the performance can be improved. The stated performance may assume that caps are present. Ceramic caps have low ESR.
Destination/decoupling. These should be near the circuits that are consuming the current.


Use the recommended caps for exact part that you plan to use. If you might use several possibilities, use the highest value recommended.