First off, congrats! I know it is not what you planned, but life is funny that way some times. (or a lot of the time!)
How long were you planning on staying for the summer? If less than 90 days I don't think you need a visa at all, as long as you can clearly show that you plan on returning to the US (letter from employers or school, ongoing bill payments, etc.)
I am not sure if you want to be married before the baby comes, as far as I know you don't have to be married in order for the baby to have UK citizenship, as long as the UK citizen's name is on the birth certificate as the parent. I am also assuming the baby will be born the in the USA since you said you are in school until next year. So, have the baby, get married (in which ever order you prefer), apply for a spouse visa a few months before you graduate/ready to leave back to UK. I am also not 100% sure on travelling with babies, I think if they are under one year they can go on the mother's passport. We have a friend who is UK and her husband is American, they got their daughter's US and UK passports when she was about 6 weeks old.
Hope that helps!