If your kids haven't learned to ride yet, I cannot more highly recommend using a kickbike. My kids all learned on them, and when they were handed pedal bikes, they were riding solo, without ever using training wheels, after only 15 minutes of an adult helping them understand how pedaling keeps them upright. The secret appears to be the challenge of bike riding is balance, and training wheels prevent you from learning how to balance. Strangely, my kids still pull out the kick bikes on occasion. They're still fun to glide around on.
My son, 9, has a Cannondale 20" MTB. 20" is the wheel size. You should get the largest wheel size that your kids can stand over, to give you the best chance of getting a couple years out of the bike. I wanted to get him something so we could ride real trails together, and this has been capable. I wasn't looking to get a suspension fork on it, but it was the same cost as one without. If you're not going to do off road riding, the fork doesn't get you much otherwise. Cole has 6 gears. Gears are very useful for keeping up with adults on family rides. His brakes are both lever operated only.
My girls, 6, have Specialized bikes with 16" wheels and a single gear. One has a hand-me-down HotRock (it was my son's, the girls trade off who gets his bike when he outgrows it), the other has a FatRock, which is basically the same, but with wider tires. It appears they've merged the two into the "RipRock". With the single gear, when we ride together as a family, they're spinning their cranks quite a bit to keep up. Around the yard, it's fine. Their bikes have a coaster brake. If the push their pedal backwards, it applies a drum brake in the rear hub. The 20" version Specialized sells also has a front lever-operated brake. This is useful for teaching them how to use the levers. One down side of the coaster brake is its tough if you go trail riding. Some times you need to move your cranks out of the way of rocks, or you need to brake when your crank isn't in the best spot.
The 3 major American bike brands that you find in most shops are Specialized, Trek, and Cannondale. They have similar offerings in each of the price ranges. They are more expensive that what you'd get in a big box store, but offer a lot of advantages. The biggest being safety. Buy something from a big box store, and it's put together by someone who doesn't know what they're doing, and the quality is junk. Real bikes will need less maintenance, and last much longer, making them great for handing down to family or selling on Craigslist (to help fund the next round of bikes!) But for that to work, you need to drill it into the kids to put the bikes away every time. Even if the frame is aluminum, a lot of the other components will rust. For my kids, it's automatic at this point.
Kids' Mountain Bikes | Specialized.com https://www.specialized.com/us/en/bikes/kids-bikes/kids-mountain-bikes/c/kidsmountain
Kids' bikes | Trek Bikes https://www.trekbikes.com/us/en_US/bikes/collections/kids-bikes/c/B506/
Kids Bikes | Cannondale Bicycles http://www.cannondale.com/en/USA/Products/ProductCategory.aspx?nid=3e7d182f-a1f7-4b7e-bde0-2f819bc4c947
The closest model to the one my son rides is listed in the "Cujo" section.
Other options common in bike shops…
http://konaworld.com/platform_kids.cfm
http://www.jamisbikes.com/usa/youthbikes.html
https://www.giant-bicycles.com/us/bikes/youth
I'm aware of one company that exclusively makes quality kids bike, but I've never seen any locally.