Yes, every doctor is different and it also depends on the situation. I was freaking out because I bled twice (just a small spot) and they made an u/s right away on week 5 and then on week 6 again (we saw the heartbeat then!!).
I have my first official appt on week 8-9 and that's when I get the bloodwork done. I didn't have any blood tests, here where I live they never do that anymore (Netherlands), they entirely trust when you pee on a stick! They also never do the hormone levels blood tests to see if baby is fine. They make you wait for a complete week and then do u/s again to measure size. I know, a bit irritant but it makes you be patient about it so I don't freak out anymore.