Ditto on the rec for giving your cat escape methods. Organize furniture so that she can climb on top of chests, shelves, armoires, desks, cabinets, etc. You could even build sturdy wall shelves like a cat walk for her to get around. And of course, cat trees.
Definitely utilize gates when you can't supervise interaction. You may just want to set your cat up all comfy in a room while the dog gets settled in and used to interacting nicely with the cat--it's only temporary and your cat would be fine. You and your SO can take turns spending time in that room.
Things to work on: "look," "leave it," "here," "stay," will all help redirect your dog. Ditto on the suggestion to play a game/flirt pole/some really great treat when he is redirected. And lots of calm praise and treats to pup when she is behaving nicely around the cat.
As far as the cat goes, really work on encouraging him to be calm/confident around the dog. Your dog probably has prey drive--if the cat flees, it will be auto-Chase until training is solid. The elevated furniture walks/escapes will help with the confidence since your cat will feel like it can get away when needed.
Lastly, a tag line on your dog will probably be helpful. You can step on it when needed or just have her with you at all times....
Oh yes, and welcome.
You'll find a lot of great articles here in the training and behavior sections. Be sure to read the stickies pinned at the top of those sections!