What you're feeling is completely normal.
Pregnancy, whether planned or unplanned, is such a huge life change, and it is scary. Having an unplanned pregnancy can be scarier in the way that it's a complete shock and you haven't really had the chance to wrap you head around the idea of having a baby yet.
The first trimester, especially, can be very tough to get through for many.
If you are in the US, first appointments can still vary from doctor to doctor.
The first appointment is still usually scheduled somewhere between the 8-12 week mark (though I think closer to 8 is more the norm). With DD, they did weight, height, blood pressure, urine sample, and blood work.
I chose a midwife over an OB. For our first appointment she went over my medical history. She asked us questions to get to know us, had us ask her questions to get to know her. We went over what to expect over the course of the prenatal visits. We received a book and some papers containing policies and information (emergency protocols, phone numbers, nutritional information, safe medications, etc).
She said she wouldn't do a pelvic exam until the next appointment as she doesn't like to meet someone for the first time and just do something so personal. She wants the patient's to meet her first. I'm not sure if all providers will do an exam. I know a lot of women who said they had one as part of their prenatal care (or not if they've had one recently) and others who say the providers found it unnecessary.
Many places will do a dating scan sometime between 8 - 12 weeks; though some places may not offer a scan until the anatomy scan at 20 weeks. This is something that would likely be addressed during your appointment; if not, it's something you can ask and they should be able to tell you.
Don't be afraid to ask questions! If you're worried, don't hesitate to call! There may be times you feel so silly for worrying, but sometimes it's still nice to have the reassurance from your provider.
If your anxiety starts to affect your day to day life, prevents you from doing daily things, please talk to your doctor/midwife about it! They should be able to offer support and resources. For some, like myself, the anxiety can get to a debilitating point and you don't have to live like that.
Just know that what you are feeling is absolutely normal. It's not abnormal to not be excited, to feel guilty, or scared/anxious. Keep open communication with your husband. While he may be feeling the same (or not), he is someone you can lean on to get through what you're feeling.