Right - it will get better! We had this exact thing, and I'm now sat on the sofa with both dog and cat snoring away beside me.
The cat going for the dog is good - you want the cat to be the one in charge. Much better than the cat running away and being a potential thing to chase.
We couldn't bring the dog in the same proximity of the cat without the cat going full throttle for the dog, so we scrapped that. We started off by having their food bowls separate by two doors, and we would open each door at the same time (while they were eating) just for 10 seconds or so, so they could see each other, but were occupied with food.
Then we brought the bowls closer so they were separated by only one door. Then we kept the door open for longer and longer, until eventually the door was open for the whole meal time.
The first three weeks when the cat wasn't allowed outside was really hard, but as soon as we got him a cat flap, and he was allowed to go out whenever he wanted, it all calmed down. And then, as he got more comfortable and settled in our house, he got more and more laid back with the dog. He still can't resist giving the dog a little swipe on his back if he's sat on the table and the dog walks underneath him, but other than that, they're totally fine. Mostly ignore each other.
The other thing to remember (which I was rubbish with, but DP did really well) was to remember to stay calm, and sound happy and relaxed. I was on edge for ages when the two were in close proximity, and DP said they were really picking up on it.