Easiest way to control a led remotely
There's many ways to do what you want to achieve - thats not to say you are naive, rather that theres different types of solutions for your use case. If you want to have it work wirelessly with a transmitter, then a microcontroller is probably best for simplicity - something like an Arduino (or even better, a Raspberry Pi, although this may increase your project in bulk) will help out, given the fact that there are wireless modules plentifully on the web - bluetooth, GSM, radio (like the 433Mhz), Wifi, many other ways.

What you want in common with all of those solutions, however, is a power source. You will almost always want to use some sort of transistor or relay to power the LED (Especially at a max of 3 watts!) - you don't want to burn out any microcontroller pins. This is achieved mostly through using a microcontroller to activate a transistor at its base (with respect to its emitter, which should be grounded) and having the LED connected (with a resistor I might add) in series with the collecter. You want to take into account any transistor power ratings too however.

Personally, I would go with the Raspberry Pi solution - the Pi Zero W is small enough to be hung from a wall charger and it can use the GPIO pins too. It should be able to interface with 433Mhz components, but its also got Bluetooth and Wifi on the Pi itself. This means that you just need an external bluetooth trigger and something like xbindkeys but for external triggers (I am not sure if this exists, but it might do). You could make a simple app (or just copy one) that turns it on or off using the GPIO pins and triggered from your input. However, I accept that it's probably overkill (though its good for scalability) so you might be better off using an Arduino instead.

If you don't want to go through that route instead, then using a wireless module (like wireless/bluetooth/Zigbee etc) built for a microcontroller (such as Pi/Arduino) will be much much harder to do, as the microcontrollers do most of the wireless demodulation, decoding etc. for you.

You haven't said what you are specifically using it for, so there could be a more efficient solution for your specific use-case. However, for just turning on a power LED from a large distance, I would say you have the right idea of a wireless module. Bluetooth might actually lose range at that distance, but so will anything else far enough. Wireless modules are cheap enough now anyway that the first port of call for many users, new or experienced, would be the Arduino/Pi and other modules.