Amp hum is usually an artifact of your pickups, rather than the amp itself. Single coil pickups (like those on your Telecaster) are notoriously noisy. Amp hum can be removed in post processing through the use of lowpass filters. Fret clicks can be treated the same way.
In almost all professional situations, studio and live, the amps are close miced. The intent is to record the sound of the amplifier as the audience would hear it, and with DI you lose a lot of the natural reverb that the room gives. If you've ever been inside a professional quality studio, you may notice that the tracking rooms are all big, spacious areas with high ceilings. That's by design, as it gives the audio coming into the space a chance to reverberate, and it is that sound that is the goal of the recording.
Volume is also something you may want to turn up. You want your gain to be as high as you can get it without clipping on the recording. Amplifiers do strange (and often very cool) things at high volume that they don't do at lower volumes (my little Kustom has this awesome bit of crunch when it's loud, for example) so you may want to capture that with the mic, too.
Generally, when you record what you are trying to capture is the sound as the audience in the room would hear it.
Anyway, I've got four new XLR cables and another mic stand on the way, so I should be able to run the sample recording soon. I'll use the Dot, as the Alncino pups in it sound great.
Someday we'll win this thing...www.aclosesecond.com