So for your first time mamas... the first appointment is not nearly as exciting as you want it to be, but it gets exciting. Basically they will take down all of your information, just like any first doctors appointment and then depending on what you choose you may or may not have a vaginal exam. I have one myself, I don't see the harm but you can choose not to if you want to be totally non-invasive. The next time you will have any internal exam will be when you are labor (if everything goes perfectly normal)!
We will be around 8 weeks for our first appointments, give or take based on your due date, your midwife of OB may want to listen for a heartbeat but probably not until your second visit. I believe (correct me if I am wrong) heart beat starts around 10 weeks.
I go a very hands off route in pregnancy and only had 1 ultrasound last time, so I don't know what is normal for your practice but I think it's fairly early for the first one. Perhaps if you need to confirm due date/ size of baby? You can always ask for one if you are dying to see, but it will not be nearly as amazing and emotional for you as it will be later on. Also be careful of your insurance benefits because some only cover a certain amount of ultra sounds for a normal pregnancy ( as in if there is something wrong, or you are high risk, you can get as many as needed)
Does that answer some questions?
Also all of you first time mamas, I know it is a tall order but try your best not to worry about miscarriage. One of the best things you can do is be stress free and relaxed, before you know it the high risk period will be over!