Couple of cheap burglar alarm IR detectors £15 (make sure they have volt-free contacts)
LED lights to go up the stairs- infinite variations, pick what you want. Easiest might be those strips you can get to go under kitchen units, cheapest probably big single jobbies from process control systems
Controller- now you've opened a can of worms. The 555/4017 combination will work but is very old-school, going to need a shedload of diodes and won't be very flexible. A random Google search led me to the Arduino microcontroller which looks like the boy to me- £25 from the worlds' favourite online tat bazaar plus £5 for a power supply so there's £30
Darlington drivers 8 channel 40p each. Depends how powerful your lamps are as to how many you need- each channel will sink 500mA at 12v but if they're all at that current for a while the thing will get hot. At that price I'd use 12 of them (one for each step) and parallel the gates (so if your power supply is up to it you can have a safe 24w per step all lit up for as long as you like) plus 12 DIL sockets £3 for 30 so there's another £8
A lump of stripboard to fix all the bits to £3
A box to put it all in £5
A drum of alarm cable (signal from PIR) and a load of 2 core bell wire £25 (outputs to steps).
A nice beefy 12v PSU (proper one with copper in it) £35 or so once you've stuck a bridge rec and a cap on it. (The cheapo switch mode ones may struggle with the load variations)
An hour or 2 learning how to program the controller
A day putting the circuit card together
Another day fitting the lamps to the staircase
So if you're doing it yourself the controller, cable, power supplies etc will cost £120 and a couple of days of your life and however much you want to spend on lamps
Have fun
This reminds me of a Contraption I had to build many years ago (198 something cough splutter). Director wanted a MASSIVE sign covered in Pygmy lamps spelling out the name of the show (CABARET), he wanted them to chase letter by letter then the whole thing to flash on and off and then back to the beginning.
We could have put it on the lighting desk but there was no automatic chase facility on it so some poor sod would have to sit there for 45 minutes (while audience were coming in) pressing the GO button every second. So I got told I was building a Device.
Cue 555 timer, 4017 chip, a bag of diodes and a load of triacs (mains lamps). Built it all nicely in a box (triacs are interesting, 240v gets where you don't really want it), tested it on single lamps- seemed to work OK, got the speed about right. Connected it to the proper sign (which was massive- about 30 lamps per letter, festoon wire and holders are so handy). Power on- ooooh look, isn't it pretty. And then it started chasing faster. And then this nasty burning smell became apparent, along with smoke out of the box. And before we had time to kill the power the thing self-destructed. Post mortem showed one of the triacs was not perfectly insulated from the heatsink, on test load the fault didn't show but on full load, 300w at 240v was looking for a home and found it on the 12v rail of the transformer.
Could have been a disaster until the old stage manager dragged out a Thing that used to power the sign at the front of the building- 10 mercury switches and a motor driven cam. Worked beautifully.
