I don't know if there is any one particular position that is best for everyone. Some women prefer to squat, some prefer to kneel, some prefer to stand and lean on something, some prefer to sit up in bed - go with what works for you! But moving around in labour is important. It will help your baby move down and keep you a little distracted. Walk as long as you can, rock, move around on the bed or birthing ball, or whatever. Don't lie flat in bed, especially not on your back, if you can help it. If you feel you have to lie down, get on your side. I would also recommend getting in the water in some way during labour. I personally found that very helpful, and I know other women have too. If there is a birthing tub, great, but if not, then try the shower, especially if there is a hand-held shower head.
Maybe look into tracking down a doula? Support and encouragement from an experienced person is proven to be very helpful in labour.
Do a little reading on labour and birth if you can, and find out what types of things you think you would be interested in, and what is permitted at your hospital.
About the gravity thing - I wouldn't want to work "against" it, but I don't think it makes that much difference. Babies don't just fall out, no matter what position you're in.
Maybe others have a different opinion on that one, though.
All the best with your pregnancy, labour and delivery!