Hi jericks,
A “comfort cradle” in that range of 3-4" certainly could work well for what you’ve described, and you’re correct that you’d want to make sure that whatever you consider has enough in the comfort layers to generally be in the range for someone who sleeps upon their side. When you’re looking online, I advise to use the knowledge and experience of reliable manufacturers and retailers who have experience with their products and what they offer that they feel would best suit your sleeping style, mass and somatotype. While their advice can be very useful, your own personal testing will be your most reliable indicator of the appropriateness of any product for you.
You should be able to find a polyfoam core or an innerspring core in or near your budget range that uses good quality materials. If you’re going to focus online, you could start by using the experience and expertise of the members listed in post #21 here who specialize in providing the type of help and guidance on the phone that can help you make good choices. There are a wide range of latex and memory foam and other options included in the choices there and I believe that all of them compete well with the best in the industry in terms of their quality, value, service, and transparency. If you have a more restricted budget, then post #4 here and the posts it links to also include many of the better lower budget online options I’m aware of. There are also quite a few options similar to what you described in the Simplified Choice thread here.
I suggest phoning any manufacturer directly if you are considering a purchase from them, and in that conversation I agree to make sure you become completely familiar with any potential return/exchange policies, should your purchase turn out not as well as you had hoped.
Let me know if you have specific questions about any mattress you’re considering, and be sure to follow the guidelines in the mattress shopping tutorial that I linked to in one of my previous replies to you.
Phoenix