I'm lucky enough to live in an area where home birth is seen as normal and even preferable, if that's what the mother wants. Even here, there are differences between midwives (some offhand, some fantastic). If you found one who was sympathetic and pro-active, track her down and talk to her. Also write to the midwife supervisor as suggested above. The important thing is that you feel confident that you will be supported at home.
Whoever is on duty comes out, and if you are dealt with by a big maternity unit, this is likely to be someone you haven't met. You can hire an independent midwife, who you can get to know well before labour - it costs about £3000, but you will only have this baby once and the experience of it will be with you forever.
Re. tearing, I had four third degree tears with my first baby. (I was in hospital by this stage - managed 27 hours at home but then went in voluntarily as was completely knackered - she was born after 38 hours, so was glad I did!) The midwives who deal with me are still very happy about home birth; they have all they need to fix you up at home, and if they can't, will know if you need to go in to hospital. My friend had a perfect home birth but managed to tear her cervix - there were no probs transferring her to hospital - it was just a shame as she was all happily snuggled in bed with her new baby.
If you labour in the bath, you shouldn't need to get out to give birth. Get some blu-tack to plug up the overflow and it makes the bath much deeper.
You don't need any special preparation for home birth, except it's useful to have old sheets and towels, plastic tablecloths and shower curtains to hand for the messy bits. The midwives will bring everything else, and all the same stuff will be available to you as if you were in a birth centre.
Don't worry about the size of your baby - no-one can tell, even if they scan at 39 weeks (which they did for me).
The "staff shortage" thing can be a problem, but it is your right to give birth at home, and their duty to provide you with care. I had been labouring for 20 hours at home (7cm) before I requested a midwife, and was told there were "none available" and would have to go in, so I got my birth partner to tell them that we were going to break into the gas and air cannister by ourselves. A midwife turned up within 20 minutes. It's invaluable to have assertive and clued-up birth partners! I had my partner and my best friend, and it was brilliant.
Good luck - home birth is fabulous - don't forget it's your body and your baby, and the professionals are there to serve you, not to order you around.