That's highly dependent on (a) your material and (b) your setup.
(a) Every material has a different cross section so the minimum thickness depends on that quite a lot.
(b) Your minimum laser focus width is also very important. With a confocal Raman microscope you can detect a lot more than width a cheap "wide laser blob" setup.
If both points are decent, you can get down very far. I mean, Raman is a standard analytic tool for graphene and that's a single monolayer. On the other hand, if your scatterer is not that great, e.g. for some ceramics, you may have a crystallite in the millimeter range and still have a bad signal.
That's highly dependent on (a) your material and (b) your setup.
(a) Every material has a different cross section so the minimum thickness depends on that quite a lot.
(b) Your minimum laser focus width is also very important. With a confocal Raman microscope you can detect a lot more than width a cheap "wide laser blob" setup.
If both points are decent, you can get down very far. I mean, Raman is a standard analytic tool for graphene and that's a single monolayer. On the other hand, if your scatterer is not that great, e.g. for some ceramics, you may have a crystallite in the millimeter range and still have a bad signal.
If you make use of resonance conditions or SERS you can have extremely thin layers. For standard Raman it is as the above answers, the scattering cross-section will determine how much material will be needed to detect a signal.
In addition to the above answers (which are all very good), resonant raman (RRS) can really make a difference: with 514 Ar laser you can nicely see a monolayer of germanium, with 633 He-Ne you'll get nothing.
Concerning general settings for good signals, the surface signal is quite often present, but overwhelmed by bulk contribution. To improve this, use high NA objectives (their diffraction cone does not go that deep into bulk and surface signals gain in relative strength) and shorter wavelength lasers (usually, blue and violet lasers have shorter penetration depth, again exciting more surface than bulk).