Meet Our New Puppy!!

About a month ago, I wrote about how I was starting to think that Matt and I should get a dog.
Matt has lots of different allergies, so we both thought we could never have a dog.
But then, I started to look into the different poodle breeds, and looked into dogs that have been ok for people with allergies.
The consensus was that pure bred poodles are the best breed for people with allergies, and they usually handle them well.
So, after lots of thought, several nights spent on the internet, two trips to a local breeder, 1 cross-city shopping trip and the hardest naming process ever, here is the third member of the Radniecki family...
Remy! She is a black toy poodle and should get to be around 6 pounds full grown.
Right now, she's maybe 2 pounds and the cutest little ball of curly fur ever.
She is feisty and sweet, and is already proving how smart she is by catching on quick to new things like going outside every few hours and sleeping in her crate overnight.
She had her first vet appointment and meeting with the groomers. She handled the new situations well with minimal whines and nerves.
Naming her proved to be more difficult for me than naming my businesses! Matt and I went round and round with tons of different names for the whole week leading up to bringing her home, and she was called by three different names in her first two days with us. But then yesterday, we decided that Remy was the perfect name for her spunky, playful self. Plus, doesn't Remy Radniecki have a cute ring to it??
I tell you what though - puppy training is no easy feat! All of you who've trained puppies before know what I mean - it is like having a new baby in the house! Except babies wear diapers.
Multiple wakeup times at night - doing things one handed or while watching over your shoulder like a hawk to make sure they don't get into anything when you're not looking... 
I was tempted to buy a Moby wrap today so I could do things with 2 hands and know where she is all the time. I figured that would be a little too much...
We are quickly learning all there is to know about owning a puppy and hope we can continue to socialize and train her well as she grows. She is 10 weeks old right now, and growing fast! 
Welcome to our family, Remy! Have you ever trained a puppy before?
Do you have any tips for us?