You want to get the F2L working well first, I would suggest the intuitive way (so many algorithms otherwise) and then you move to the LL. My friend is still doing a basic LL + F2L and he can get to about 36 secs, he has an amazingly fast LL, for basic method.
Very much so intuitive F2L first. Get a basic understanding of how pieces work. At the same time learn 2LOLL. You already know at least three of the nine algorithms, that means you need to learn six (although you might technically have to "learn" the 2nd EO alg because you probably do F RUR'U' RUR'U' F' instead of f RUR'U' f' ). Anti Sune, H, Pi, Bow Tie, and Chameleon are all easy to learn