It's the details that cost. It's also the details that make it special.
First, you need to find a quilter who has a sewing machine that will do embroidery. Not all of us have them. They're computerized, and the machine embroiders a multi-colored picture. I don't have an embroidery machine, but I'd guess that the more colors in the design, the more a person would charge for the design, because she has to do more work in changing colors and making sure the picture lines up right to add the next colors. But you might get lucky with finding someone who is very skilled and doesn't charge extra for it.
The pictures on the page I looked at range from some very easy ones, to some more complex ones. The alternating 6" squares would be cheaper than anything using small pieces. Small pieces take longer to cut out, longer to sew back together, and there's more fabric wasted in seam allowances. I'm working on a quilt using some 6" blocks, and I was astounded at how quickly it went together.
Then, there's the quilting. If you're working with someone who has a longarm quilting machine, she will be able to do this faster than someone who quilts on a regular sewing machine. However, that varies, with the skill a quilter has using the machines! So you might find someone who is really skilled with a standard sewing machine, as opposed to someone who just bought her longarm and is still learning how to use it. Then there are people like me, who hire quilters to machine quilt for them! So don't assume that because someone knows how to piece a top, she'll be able to piece a quilt AND finish it for you.
I'd recommend that you attend quilt shows and craft shows, looking for something you like, and then ask the maker if she takes commissions. Or check for a local quilt guild, go to a meeting, and ask. Hunt quilt pictures on the Internet, and take a folder of ideas with you, like you'd do if you were going to a new hair stylist. Ask what sorts of fabrics she wants to use, whether she wants you to buy it, and where she will buy it. There are Internet stores like Hancocks of Paducah that sell top-quality quilting fabric for less. Many of us will not agree to work on cheap fabric because we know it won't hold up long-term, especially for a kid's quilt which is going to get wallowed around upon and spilled on and washed more often than an adult's quilt.
Quilters love the idea of making quilts accessible to the next generation.
I don't do quilting for hire, but I'll bet there's someone out there who will be charmed with the idea of making quilts for your kids, and who will help you work out a way to get it done.