If any energy saving deserves the phrase fit and forget, it is LED lighting. The bulbs sip electricity, last for years, and the swap pays for itself quickly and then keeps paying with no further effort.
The saving
An LED produces the same light as an old incandescent or halogen bulb for a fraction of the electricity, often around a tenth to a fifth. Lighting is not usually the biggest line on a bill, but if you still have halogen spotlights, which are notorious energy hogs, replacing a roomful makes a visible dent, and the bulbs last so long that you rarely change one again.
Choosing them
Ignore watts and look at lumens, which measure actual brightness; roughly, 800 lumens replaces an old 60-watt bulb. Colour temperature is a matter of taste: warm white around 2700K for a cosy living room, cooler white for a kitchen or workspace. Check the fitting matches, and if the bulb is on a dimmer, buy one marked dimmable, since a non-dimmable LED on a dimmer flickers or buzzes.
The few cautions
Very cheap bulbs can be a false economy, dying early or giving poor, harsh light, so middling quality is worth it for something that should last years. Enclosed light fittings trap heat and shorten an LED's life unless the bulb is rated for enclosed use. And dispose of old fluorescent tubes properly, as they contain a little mercury; ordinary LEDs do not.
Just do it gradually
There is no need to rip out every working bulb at once. Replace the ones you use most first, the kitchen and living room, then swap the rest as they fail. Within a year the house is done, the lighting bill has shrunk, and you have stopped buying bulbs.