spaying a dog - ovariohysterectomy, or ovariectomy?

So, I am a new puppy owner, and have fallen head over heels over my new little girl... it is time to have her spayed, and I need a ton of reassurance please on the procedure. I've read that in the States, it is very common for ovariohysterectomy to be performed. I have also read about another procedure where just the ovaries are removed. This is a less invasive surgery, and is the more commonly performed procedure in Europe. Recovery time is faster, and less possibility for complication. 
My vet (who I like, but I don't know any other one, this being my first dog) does the full ovariohysterectomy. She is a small dog, very sweet and I feel overprotective, lol. So, as I'm researching, I read the best thing if you are getting everything removed is that the dog is on fluids during the procedure and they should have bloodwork taken beforehand. My vet doesn't do this unless there is some concern prior to or during the procedure. Can I hear some stories of what procedure you had done? What did your vet do? Do you have any regrets, or wish you had done something different, etc. Have you had the ovariectomy? Thank you from a nervous pet parent!

Aren't you cute.

If only the tubes are tied, does the dog still have a period?

My neighbor's dog just got the full spay, was in cone for 3 days, and was back to playing in 5 days.

I think you’re giving this way too much thought. It’s a simple, very basic, very common surgery. Recovery time is quick. It’ll be fine.