Your "transistor as a switch" circuit should work fine. Try it out!
One characteristic of transistors you should know about is that they have what's called "gain". Which means a small current flowing from base to emitter can control a much larger current from collector to emitter. The BC547 has approx 100-800x current gain, so you could use a much higher resistor on the base and the transistor will still turn on fully. For example, a 100K resistor would work, though 10K is more commonly used to ensure the transistor is fully "on" even if you're switching larger currents. For your little LED, a higher base resistor will work no problem.
With your circuit using a pot, you can see how the transistor responds over its "linear region" as well. This is the region in between "fully off" and "fully on". When the B-E voltage reaches 0.55V or so the junction starts to conduct and the transistor starts to turn "on". At around 0.7V it will reach saturation and be fully "on". This is a narrow range near the bottom travel of your pot, where it transitions between fully off, partially on, and fully on.
Since a transistor can control a much larger current using a smaller current, it works as an amplifier, like those in radios, cell phones, etc., and it can also be used to allow a small voltage/current to switch on/off a larger current.