In my opinion the overhead of LCDs is not their cost, but the extra work involved in connecting them and programming them. I see many sketches here where the problem is completely obscured by LCD code.
Leave the LCDs until you have a working system.
To learn about the timing process I suggest you write a short sketch which uses a few LEDs to simulate the different phases of the process. Write the initial code with short timings of a few seconds per step so that you can easily run through the whole process without needing a coffee break :). When it works you can increase the timings.
In case it hasn't been mentioned look at the technique in the Blink Without Delay example sketch. I have written a more extensive example here.
I have several LEDs with a resistor soldered to one leg and an extra piece of wire (the same length as the resistor) soldered to the other. I can plug them directly into the Uno or into a breadboard for quick and dirty testing.
...R