We gave Millie the regular sippy cup, but removed the thingee from the underside of the lid, the thing that makes the lo have to "suck" to get a drink. Someone told me that it was exactly the same thing as a bottle if they had to tip and suck....idk why that made sense to me at the time. It is typical that they will bang it and throw it for a long while...we intrduced the cup at about 9 months...it took a bit of time, but she got there. My dd couldn't suck from a straw until about 10 months.
Just keep it in play, keep it in the landscape of things that she sees and experiences every day...she WILL get it. You're offering at every meal, that is great!