According to everything I've read, there is no real point in trying to alter the way you breathe. I believe some guided relaxation 'meditations' use this technique of counting in and out breaths is to kinda force people to slow down their breathing, but for normal breathing meditation you just breath normally.
There is no such thing as a blank mind (as you'll find out when you start to meditate!
). You're not trying to change the thoughts that come in and out of your mind, and you're not trying to stop them (that's impossible). You're simply observing them, mindfully. If they're happy thoughts, that's fine. If they're scary or dark thoughts, that's fine.
Personally I try and just observe anxiety symptoms too, although if I'm in the middle of a bad anxiety attack I would rather just breath slowly whilst uttering my mantras - 'this will pass', 'I'm in no danger' etc etc. I could do this for 5-10 minutes before starting to meditate.
As for length, I think anything you can manage is fine, even if it's just 2-3 minutes. My own personal guide right now is 10 minutes, which I set an alarm for.
My experience recently is that for the first 5-7 minutes my mind will be racing, thoughts come and go very quickly (10-20 a minute usually) and sometimes I'll get stuck on a thought for a little while before I realise that's what I'm doing and guide myself back to the breath. Then I feel a slight change, I can feel the mind slowing down a bit. I find it easier to focus on the breath (but remember, even recognising that it's getting easier is just a thought to be observed!).
I once read a book that gave the analogy that the mind is like a cup of liquid that's been agitated. Even if you sit down and try and relax, the thoughts in the mind (the liquid) can still slosh around for a while. Mediation is the act of creating the conditions of stillness that allow the thoughts (the liquid in the cup) to naturally settle. That act of refocusing the mind on the breath and not reacting to every thought is just that. With practice, you will feel the 'noise' start to dissipate.
I realise I say quite a lot on the subject, but it's taken me a long time to gain the knowledge that I have now and I've always wanted to find an answer without medication.
The key thing to remember is that if you're trying to meditate and your mind is racing, if you feel like your trying to focus on the breath isn't working, that's fine. It's the act of trying and practising that will net you results. It doesn't have to feel like it's working to actually be working, just like jogging to lose weight.