It sounds a bit patronising to tell people that they need to learn how to hold a cube properly. But this is probably the single biggest mistake I made when starting to learn speedcubing.
I didn't even think about how I held the cube until after I'd learned a whole load of algorithms. Then I realised that I needed to hold it a different way if I was going to execute the algorithms quickly. And guess what happened... when I changed my grip and hand positions all those muscle memories I'd built up were wrong... I found myself going wrong all the time in the middle of algorithms that I thought I knew really well.
In the end I had to effectively relearn a lot of what I had learned.
So, my top tip is start off with the right grip and hand positions and save yourself the trouble of relearning all those algorithms later!
Alex Lau has a great video (only 2 minutes long) showing how to hold the cube and do finger tricks.
He is a seriously fast cuber (I have seen him competing a few times) and knows what he is doing!!!
For the algorithms I am going to suggest later, you should concentrate on R, U, L and friends (R', R2 etc) ... with the odd F, F', D and D'.
I never use B or B'. One algorithm I use has one Lw and one Rw'. A couple of algorithms for the last layer have M and M2 moves.
