Congratulations to you both! I have twins (8 now) and the pregnancy was actually easier than my current one (with one baby). Increased morning sickness is normal but not inevitable. Extra scans are likely (lots of extra scans if they share a placenta). Having twins is great, though.
I'm 28 weeks with ID twins. From what I can gather there really isn't a major difference in care apart from the fortnightly scans which become a little boring after about the 5th one. From what I can gather, the major diffrerence is stress on your body. Worse morning sickness, more painful back ache as you just grow likely crazy from about 22 weeks onwards, there are a few illnesses that you are more prone to like PUPPS and TTTS (if they share the same placenta). You should look them up as I have PUPPS at the moment and although it's pretty harmless it did freak me out at first. Apparently it's really common with people carrying twins. And you do have an increased chance of having a C section as they don't always behave and lie in a good way for delivery. Otherwise congratulations and take it easy, you are really going to need that extra energy ;)