Be very careful feeding grain free to a puppy. Many of the mainstream brands are NOT for pups. EVO for instance does not reccomend feeding to puppies. And CORE says right on the bag not for pups under 1yr. A few brands have grain free puppy formulas and those should be ok. And some say All life Stages, those are ok too. Be sure to read the whole bag, and do some extra research if you want to feed grain free to a pup.
I'm assuming by your description that the website you are using is dogfoodanalysis.com? I like the site but don't always agree with them. In my opinion, anything that merits 3 stars or better on that site is a good food. I don't think you should feel guilty for choosing a 3 star over a 6 star. Get what you can find firstly, a food is no good to you if its not available! The difference in quality above 3 stars really starts getting picky. And, in many cases, there are other considerations, like the company and its past history, ingredient preferences, price etc that should go into the decision.
Some common, economical foods are-
Chicken Soup For the Dog Lovers Soul (hokey name, good food)
Kirklands (Costco's house brand)
Canidae (this is an all life stages food)
A bit more expensive is stuff like-
Taste of the Wild
Thats by no means an exhaustive list, or even a list of the best. But all are quality foods that seem to be commonly available. In my experience, Innova and California Natural has been reported to be a little rich for puppies. Those seem to work better for adult dogs, although I also know folks who raise pups on it and love it.
To switch, you'll want to start gradually. I'd let your pups digestive system guide you. Some dogs need to switch VERY slowly, others do fine with a faster switch. The plan listed above is a good way to start- 1/4 new food and 3/4 old food. If his stomach seems upset, you can start with an even smaller amount, say, 1/8 new food and 7/8 old food, and then gradually work up.
A few days or weeks of proplan won't kill him, and a sudden food switch in addition to moving to a new home could be a shock for his little system, so don't feel too bad about taking your time to make a food choice.