I, too, am jumping on the "light my stairs" project bandwagon.
I know very little about Arduino so, please be patient with this noob.
I'd like to have a sensor and light at each step. My questions:
Is this possible with Arduino? If so, which board/s would work?
What would be best sensor to use? pressure? IR? light beam?...(cost is, of course, a factor)
When someone is on a step, and the light is activated, is it possible to have another step/s lit for another person? Eg; two people walking on the stairs, and each step is controlled individually.
Any ideas on what lights would be good to use? (L.E.D. of course, but, type? number per stair? optics? power supply?...)
Next time you go up or down a stairway try to imagine what it might be like if you could only see the step you're on, and the next one - it would be almost impossible to use the stairs safely at any reasonable speed. Your idea is easy to implement - running an LED or relay from a switch is simple, it's one of the example codes. Use of a shift register is in a lot of beginner kits too.
http://arduino.cc/en/Tutorial/Debounce (how to read a momentary push button - it's called 'momentary' BTW, all switches are 'reactive' )
http://arduino.cc/en/Tutorial/BarGraph (controlling lots of LEDs)
The answers to your questions about numbers of lights and such will affect your circuit design. As mentioned above, every circuit is limited to a certain amp draw, above which the components will usually melt or fail in some other way. So, you kinda have to design your lighting, figure out how many LEDs and what type, then you can pick your control devices. LED strips add up fast! Each LED usually pulls 20 milli-amps, 60 per segment - so three segments is the limit to how much the Arduino can control by itself, and that's also the limit of each pin on the shift register mentioned above. However, three segments of white LED strip is pretty darn bright, more than enough to light a stair step. One segment on each side would probably be bright enough. You are going to need to decide what to use though - we can't see your steps.
I did a video about LEDs a while back - I explain the drawbacks of the strips and why you might want to hand-wire your LEDs. The main issue is the strips need to run on 12V.
This shows some different types of LEDs, how to wire them up, how to solder them, how to design your circuits and so on.