Landau/Lifshitz is simply overkill for getting started in learning physics, especially since you are planning to do this on your own.
In general, you need a book that takes you by the hand and has a lot of worked examples in it. Most physics text books include exercises, but they do not give you worked solutions.
There are some text-books to which instructor solution manuals are available online, if you get what I'm saying. If you really want to learn physics, you need to do physics, i.e. calculate, think, calculate, think, calculate think...
You having an electrical engineering background, I would recommend you get started with electrostatics and electrodynamics, since you can relate and it is always easier to start with something that you can relate to.
A good place to start is this script by Uppsala University on Electrodynamics which has a lot of worked examples in it and is written extremely clear (plus it's free).
A good book to start is Griffiths Electrodynamics, since you can obtain a solution manual for the exercises by asking around and it contains worked examples.
Once you have mastered all of this, you can go on to read Landau/Lifshitz to prove that your are not a sissy ;-). Most of my professors include Landau/Lifshitz in their lecture notes, but when it comes down to really learning something from the scratch, we always go to more modern textbooks.
Concerning the prerequisites to read Landau/Lifshitz, maybe this is helpful:
Landau developed a comprehensive exam called the "Theoretical Minimum" which students were expected to pass before admission to the school. The exam covered all aspects of theoretical physics, and between 1934 and 1961 only 43 candidates passed.
Taken from Wikipedia entry on Landau.