All the answers for your questions depends about somethings, like this:
- What Transistor would you use?
- You want to control the load current (limit the load current) or you want that transistors operates like a fully on switch?
To dimensionate the resistors, you will need to read the transistors datasheet, and search for the hfe or β, the amplification of the transistors. So you will use:
Ic = β.Ib, find the Ib and then find the base resistance by Ohm's Law. Remember that you need an Ib greater to the Ib calculated to operate at the fully on mode.
Finnaly, you will find a graphic like this on the transitor datasheet:
So you can obtain the Vce voltage (transistor voltage drop), after you dimensionate your base resistance (you will know Ib);
If you get your load equation in function of the variables I (Ic) and Vce, you can construct another curve into the above image, like below:
Example: If your load is a Rl resistance, you will get the equation:
I = (5 - Vce)/Rl
So you will determinate whit precision your Quiescent point, that is the point of operation of your circuit!
Just a tip: Do you know any Spice simulators? Whit them you can simulate your circuits, whit a model for each component, and discovers how your system will work at many situations, it's a very useful tool! I use the simetrix simulator!