Hi CatCuddler,
Welcome to the Mattress Forum! 
While I can help with the “how” to choose a mattress, I can’t predict “what” would be best for you. The first place I would start your research is the mattress shopping tutorial here which includes all the basic information, steps, and guidelines that can help you make the best possible choice … and perhaps more importantly help you know how and why to avoid the worst ones.
Two of the most important links in the tutorial that I would especially make sure you’ve read are post #2 here which has more about the different ways to choose a suitable mattress (either locally or online) that is the best “match” for you in terms of “comfort” and PPP (Posture and alignment, Pressure relief, and Personal preferences) that can help you assess and minimize the risks of making a choice that doesn’t turn out as well as you hoped for and post #13 here which has more about the most important parts of the “value” of a mattress purchase which can help you make more meaningful quality/value comparisons between mattresses in terms of suitability (how well you will sleep), durability (how long you will sleep well), and the overall value of a mattress compared to your other finalists (based on all the parts of your personal value equation that are most important to you).
The first “rule” of mattress shopping is to always remember that you are the only one that can feel what you feel on a mattress and there are too many unknowns, variables, and personal preferences involved that are unique to each person to use a formula or for anyone to be able to predict or make a specific suggestion or recommendation about which mattress or combination of materials and components or which type of mattress would be the best “match” for you in terms of “comfort” or PPP (Posture and alignment, Pressure relief, and Personal preferences) or how a mattress will “feel” to you or compare to another mattress based on specs (either yours or a mattress) or “theory at a distance” that can possibly be more accurate than your own careful testing (hopefully using the testing guidelines in step 4 of the tutorial) or if you can’t test a mattress in person then your own personal sleeping experience (see post #2 here). Generally, someone sleeping upon their side would want to make sure any mattress they were considering offered enough surface conformation to allow their shoulders and hips to sink in a bit while still offering enough support to maintain a more neutral alignment.
As you mentioned you wanted to keep your price lower, for those on a more restricted budget post #4 here and the posts it links to also include many of the better lower budget online options I’m aware of as well.
I hope that helps you get a good start on your search!
Phoenix