Say for instance, the goal is to light an incandescent bulb for x amount of seconds (let's say 20).
What is the simplest configuration possible?
Of course, simple timer circuits aren't rare, and can be found easily online. A simple search engine query will show this. The thing is; they often vary in the number of components, and their configuration. As far as I can tell, the extra complications often seem superfluous and unnecessary, if the same goal can be achieved without them.
If you'd like an example, here's one that I came across on this site, for a 30 second timer.
Okay, so everyone seems more focused on my commentary than the actual question. I'm happy to discuss things, etc. But my priority is answering the question.
So to bring the focus back to the initial goal, I'm sharing my first attempt at a 20 second timer. I tried to make it as simple as possible. And the values are totally wrong. If you couldn't tell, I'm new to this, and don't fully understand everything yet, so please be kind.
This is my schematic.
I think it was originally an attempt to make sense of this page, via chance & data; trial & error.
Answer
Don't confuse the circuitry for the timer part with the remainder of the circuit.
In the example you gave the components shown left of R3 are actually there to de-bounce the push button switch which presumably was a critical issue for this designers application.
The remainder is your typical 555 one shot circuit, with decoupling, a power on reset delay, and of course a load LED.
Designers seldom add components for no reasons, in fact, usually we strive to eliminate components.
Sometimes the wisdom of what is added to perform some function can be a bit suspect however.
Update
Your schematic for a simple timer is correct, but the values are way off for a 20s timer.
The formula for the time period of a one shot 555 timer is the standard equation for the amount of time it takes an RC circuit to charge up the voltage on a capacitor to 66.666 % of the final voltage.
\$T = 1.1 * R * C\$ or more accurately \$T = 1.0986 * R * C\$
Since capacitors come in more limited sizes, pick a reasonable capacitor value first, based on cost and dimensions. Since you want a fairly lengthy pulse, lets pick \$100uF\$.
So now we need to calculate a value for \$R\$. Rearranging the formula above you get.
\$R = T / (1.1 * C) = 20/(1.1 * .0001) = 181,818.818...\Omega\$
Round that to the nearest E-Series resistor 180K. (quick check T=19.8 Seconds).
At this point we normally sanitize the answer. That is, if R is ridiculously high, eg > 10M, or far too low, we would chose a bigger or smaller capacitor and redo the math.
TIP: A shortcut to do this quickly is simply to multiplying the cap by 10 while also dividing the resistor by 10, or vica-versa.
So here is your 20s timer circuit..
simulate this circuit – Schematic created using CircuitLab
Remember there are part tolerances involved so, with 5% parts your timer will be anywhere in the range of 17.85s to 21.8s.
If you need it more accurate than that, use 1% parts and possibly add a trim-pot in series with the charge resistor. However, be aware, the period will change with temperature.
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