Light up an LED on turning on circuit
simulate this circuit &ndash; Schematic created using CircuitLab
D2 - I couldn't find a Schottky diode symbol.   Some folks would use a silicon diode here (i.e. 1N4001).   I prefer a Schottky because they're faster.   D1 can literally be any 3 or 5mm LED you find, they'll pretty much all have the same 20mA maximum.  Using a 1k resistor will keep the current well below 20mA so you'll have no issues there.
I suggest using a &quot;diffuse&quot; or &quot;milky&quot; LED instead of clear because they make better indicator lights  (i.e. if your intention is to look at the LED, use diffuse.  If your intention is to project light elsewhere, use clear).  So don't be fooled by brightness numbers - You don't really want something that blinds you if you look straight at it.  (Clear LED's have massively higher brightness specs, don't fall prey to that)
Note any color LED will work here, the 1k is universal enough of a value you won't have problems.  (That is NOT a universal statement... 1k is good enough HERE)