In the US, it's pretty common to have your first appt around 8-10 weeks. It is not necessarily routine to have blood work first. My experience (which seems common) was the first appt involved a long talk about my medical history, and answering questions I had. It is common to also have an abdominal ultrasound as part of this appt. They should definitely not need to do a vaginal at that point unless there was some problem with the baby being MUCH smaller than expected based on your last menstrual period.
Once he confirms the viability of the prgne with ultrasound, my doctor then goes over what additional tests and scans are available or appropriate based on your risk factors (age, family history, etc), and lets you know when/how to schedule them. He also gives lab orders at that point for some routine blood work to check for thyroid problems, HIV and a few other things.
It seems like the frequency of ultrasounds varies a lot with different doctors. Mine usually does the initial one, then sends you to a more advanced office for a very detailed scan of baby's anatomy around 20 weeks (part of this did involve a vaginal scan, but it was not mandatory and not that bad), and then he does one more to check for growth around 35 weeks. Of course, they would do more if there was some perceived need (like suspected slow growth, low fluid, breech position in last 1-2 months). I ended up getting two additional ones - one was specifically to examine a potential problem with my son's heart (thankfully all was fine), and the second was bc they thought he might have gone breech at 37 weeks (he hadn't, just had a bony bum that felt like a skull). However, it seems like some people get them at almost every monthly appointment.