First question: Find a balance. Focusing on one or a few moves at a time will definitely be beneficial in several ways, most of all in terms of motivation. If you never master any moves, you won't see as much tangible progress and are more likely to lose interest. Then again, do choose moves (or flourishes) that you WANT to learn, as this is equally important for your motivation and enjoyment.
My standard recommendation, and what I did, was start with charlier cut and/or thumb cut and/or any other simple cutting technique. At the same time, select one or two harder flourishes that you really want to get good at, like thumb/pressure fan or a card spring. This way you have something easy that you should make good progress on quickly, while also starting a longer endeavor towards a hard, prestigious, and really rewarding move.
Something else that is nice to learn is proper shuffling and bridging, which can be busted out whenever you play cards without being too "show-off-y" since you have to shuffle the cards anyway.
Title: It's a slight limitation, but nothing you should be particularly concerned about. As you progress, you'll notice that the fingers and hand can stretch more and get stronger in stretched positions as they attain more muscular control.