If you web-search 'simple circuit' and look at images you will find a wide range of potential examples.
Start with eg Simple circuits google search.
Ideas here but less useful "everyday".
Bonus - I decided to try to locate the origin of the circuit below.
I found that sadly the originator, Tony van Roon died in 2011, but he has left a marvellous legacy of simple and often useful circuit. These are older circuits - well back into last century in some cases, and suitability for purpose needs to be checked in each case (but at a glance most seem bearably OK). As idea starters for modernisation they are excellent.
This web search turns up many of Tony's circuits.
Indexed list of Tony's circuits
Here is one-only which seems to meet your criteria - and it has the added bonus of being potentially useful.
This is a lead acid battery charger connected to an emergency light which is turned on when the input power source fails / is removed. The charger is everything to the left of the battery. The circuit has 20 components (excluding the battery) and all components are relatively common and/or could be easily substituted with similar ones.
The left to right functionality flow will tend to help keep the layout simple.
18 VDC (NOT AC as it says) power in at left. LM317 provides regulated voltage with Vbat set by R3 R2 P1 and adjusted by P1.
Q1 R1 R4 sets maximum current.
Ra turns light OFF when Vin is present.
When Vin removed Rb turns BC557 on which turns 2N3055 on which lights lamp.
Lamp could be a suitable LED(s) + resistor.
Transistors at right could be FETs .
Q1 must be bipolar.
Het sink for the circuit shown above.
This is only an example circuit BUT this shows what the PCB designer needs to allow for.
It has been suggested that adding a heatsink for the TO220 packaged regulator may be difficult for a beginner. A heatsink can be a simple L or U shaped piece of eg Aluminium with the TO220 package mounted flat and fixed with a single 3mm screw to the PCB. Or the heatsink and TO220 package can be mounted vertical. The small tabs seen on the 12 C/W heatsink below may be placed in holes in the PCB - or may be removed with a degree of loss of mechanical stability.
At say 1A load current the LM317 would dissipate 1 Watt per volt drop and the temperature rise for the 12C/W heatsink would be about 12 degrees C per volt of drop. For say 60 degrees C delta a 5 Volt drop would be allowed. So about 16 V in max DC with the battery at 11V.
The shown 18V in is unnecessary and also would need a larger but not large heatsink.
For much more on this site on TO220 and other heatsink design see here