Generally the first appointment will just be confirmation of pregnancy. The doctor will collect a pee sample from you, and then probably need to get some information from you, such as the date of your last period. You might get a bedside ultrasound, which is usually very low resolution, and you may or may not see anything depending on how far along you are. Then they'll probably schedule a viability/dating ultrasound for you as well as schedule your next prenatal appt in a few weeks (usually they will want to see you every 4wks).
Normally, your doctor will get a pee sample for testing to confirm if you're really pregnant or not. It will also depends but most probably, your doctor will schedule an appointment for your ultrasound.
Re: Positive home pregnancy test