Hi!
Congrats on the new addition to your family!
definitely ask the shelter what they feed and see if you can buy a small bag of it for your new doggy. Mix that with your new food over the course of about a week, putting more of the new food in by the end of the week, so it won't upset your yorkie's tummy. Try doing 3/4 old, 1/4 new then 1/2 old 1/2 new then 1/4 old 3/4 new and then all new. Make sure to read the amount you should be feeding per weight on the new food and stick with it!
I definitely recommend kibble (dry food) over wet food. Dry food can help keep their teeth healthier with its texture and crunchiness. Wet food is great as a treat and to help up their appetite when they're sick, but I don't recommend it as the whole diet. I also don't recommend mixing it with dry food. That usually makes dogs pickier and they only want dry mixed with wet and they won't just eat the dry by itself. However, all dogs are different! I say this from my own experience and the experiences of my customers at the pet stores I've worked at.
As far as brands, stick with holistic brands. Avoid grocery brands and anything containing corn and wheat; soy too, if possible. My yorkie eats Blue Buffalo Wilderness for small breeds. It's a shiny pink bag! She loves it. I've also fed her Wellness, which she loved until she grew tired of it. Nutro Ultra is also decent, though I no longer buy Nutro because of their yearly bag size decrease/price increase. Healthy nutrition is very important and while it may seem like a lot for food, the results are worth it. I have always fed my baby healthy, holistic, all natural foods and never had any major health problems. It's an investment in your dog's health. I work at Petsmart and we sell these foods, though I'm sure you can find them other places.
For treats, go with healthy too! Mine loves the Nutro crunchy treats (blueberry and apple, specifically), Wellness soft treats, salmon treats, and Blue Buffalo soft treats. I really like the tiny Bil Jac treats for training too.
I hope this helps!! I love helping new pet parents find healthy things for their fur kids! Message me if you need any more help!!