Design a timer circuit
I would forgo using any analog components for the time-keeping process and just use a microcontroller. The benefits are as follows:


Simple to modify/adjust time intervals
Easy interface into 7-seg display / beeper / lamps
Good timer accuracy/range


The only analog circuits you would need are simple transistor drivers for the lamps. Using a microcontroller (like your mentioned arduino) would nicely separate the functionality into behavioural blocks. This helps organize your project, when debugging it, and when showing it off.



If you're dead set on the 555 it will be harder. Long time constants require large capacitors and/or large resistors. This may cause leakage currents from the 555 to cause timing issues. Additionally, component tolerances will muck with your timer accuracy. Depending on your adjustable timer setting, implementation might get even more complicated.