How quickly do you learn?
The only real answer is that you need to practice until you either become competitive in your chosen class or until you realise that you can't dedicate enough time to become competitive in your chosen class... and you'll only know this from your own personal rate of progress.
In my estimation, running a few packs a week will not be enough. You need regular and "recent" practice to learn. This is to say that every practice session should be close enough to the last that you can actually remember the last - what you experienced, the mistakes you made and more importantly the "feel" you had.
"Feel" is that intangible thing that connects you, through your radio, to your car. The ability to predict what the vehicle is going to do next and react (appropriately) to the prediction rather than the event... when you're doing that you know you've practised enough.
It depends on what you want to achieve. I would think ~40 hours of practice would allow a competent learner to be competitive in club racing (although this doesn't mean A-Main victories!). Open classes are a different matter - if somebody knows how to whip a 6.5 around a track quickly then no amount of practice will beat them if you have a 17 installed.
Mini class is a great class to learn really good RC driving in.
Edit: Tip - don't learn the track, learn the car. If you think you're learning more about the track than the car then take it to a parking lot and switch it up some.