I think 2K is the maximum sum you need to spend on learning.
Private learning will be cheaper, probably $25/1hr lesson.
Organized learning will cost you around $65/1.5hr lesson.
Most learners require around 30 lessons. Booking the warm up
session and test should cost you another $150 or so.
Just make it a point to set aside $300 a month for now, so you can
get a decent one lesson per week. I don't see why you need 3K in
the bank before you can give it a shot at getting a license.
Extra lessons conducted by helpful friends should of course, speed
up your learning process.