Hi sleepy_jan
Welcome to our Mattress Forum! 
The first suggestion I would have is to start with the mattress shopping tutorial here and make sure to you find out information listed here so you can compare the quality of the materials and components to the durability guidelines here to make sure there are no lower quality materials or weak links in a mattress that would be a cause for concern relative to the durability and useful life of a mattress before making any purchase.
You are correct that children need a sleeping surface that is more supportive due to their epiphyseal plate and postural formation. As you seem to be looking for something using polyurethane and Memory foam, I’d want at least CertiPUR-US certification for each of the foams used in the mattress. You’ll tend to find your best price with traditional innerspring style mattresses for this particular application. Post #2 here includes links to most of the better forum posts and topics about mattresses and children and includes some suggestions and guidelines and links to some good quality/value options as well.
The mattress you mentioned is a 10" mattress containing 5" of pocket coil support layer and 4.5 inches of various foams of unspecified densities, which usually is a sign that there are lower quality foams that will break over time and cannot serve as a base for further adjustments as the child grows. With any mattress, you are considering, but especially for children, I would also make sure that all the foams listed in the mattress have safety certifications. As an alternative, you could checkout NestBeding 7" Big Kid’s Bed mattress which is in your price range and uses good quality and safe foams. They are also one of the our Trusted Members here which means that I think very highly of them and that I believe that they compete well with best in the industry in terms of their quality, value, service, knowledge, and transparency.
While adults can do better with memory foam …I am always hesitant to recommend this as a choice for children and Post #2 that I linked above has more about choosing materials that are “safe enough” for children. Children also do better with more freedom of movement than even more responsive memory foam can provide. Aslo … the microclimate of a memory foam mattress is not as breathable and temperature controlling as other more breathable materials and I believe that children need every advantage we can give them while they are sleeping, growing, and developing. Even with grownups, there are some guidelines that should be followed to make sure that you know what you are buying and that you can lessen the risk of buying memory foam in a very confused market that will supply you with lots of misinformation.
In general, for a growing child you won’t really need more than about 6" or so in thickness if you get a component style mattress when they grow older if they need some additional thickness or softness then you can either add another layer inside a new cover (if you have a zip cover) or add a topper to the mattress. One of the advantages of getting a multi-layered component style system mattress is that you can add or exchange layers as your child grows. If and when they need a softer comfort layer in their “sleeping system” you can also add a softer topper to any firmer children’s’ mattress when they get older and develop more adult proportions. If you desire something more “natural”, but want to keep the cost as low as possible, you could do something like this (SleepEZ, roma) or this (Arizona Pr) both trusted members of the site. There are of course other options out there, but I’m familiar with these. As the child moves from the preschooler/early childhood stage into teens it is usually recommended to adjust the sleeping surface towards the medium firm to medium (although growing children can adapt to almost anything) but you’d still want to keep it a bit “firmer”.
I hope this gives you a good place to start.
Phoenix