Correct resistance for a transistor?
If by "turn on completely" you mean "produce 1 volt across R3", the answer is "none". As in "not going to happen." The best you'll get is about 0.3 volts, which corresponds to a 0.7 volt drop across the base-emitter junction. If you want 0.9 volts or better across R3, you'll need to change your circuit to 







simulate this circuit &ndash; Schematic created using CircuitLab

then $$R1 = \frac{1 - 0.7}{10 R3}$$ as a first approximation. This works from the assumptions that a) the transistor can be driven into saturation with a Vce of less than 0.1 volts, and b) providing a gate drive of 1/10 the collector current will produce saturation, which is equivalent to saying that the gain of the transistor in saturation is 10, which is a standard rule of thumb.