steph, you should have a look at the bf/bottle feeding section on here, there is loads of advice.
I am bf my ds who is 7mo. I have fed him in pretty much every cafe/park/shopping centre in my local area. I am quite self conscious and was worried about feeding in public, but I think once he was born I just stopped caring what people thought - he is hungry and needs to be fed, that is that! I have never had a funny look or comment from anyone - you can't see anything anyway - a screaming hungry baby is far more noticeable.
WRT your partner - there are plenty of other things he can do with the baby - cuddle, sing to, talk to, bath, change, massage, etc. BF is so beneficial for your baby and I'm sure your partner will be mature enough to see that the benefits of bf outweigh his own desire to feed the baby.
I would give it a good few weeks before expressing at first. Then you can see how well you get on with it. I can't really be bothered with it, find it a bit of a faff and much easier to feed, although on the 4 nights out I have had since my ds was born, he has taken ebf from a bottle no problem (although this might be unusual).
Def find out if there is a bf group near you.