Hi AdrienneH,
There is really nothing “wrong” with an innerspring mattress for side sleepers and the choice of materials and components in a mattress is really a matter of preference. Any type of components (innersprings, polyfoam, memory foam, latex, or other materials) can be made in a way that is suitable for different body types and sleeping positions. It’s much more a matter of the design of the mattress being suitable for you than the type of materials used. having said that … latex is certainly a very high quality and durable material.
Foam mattresses generally do much better with a firm non flexing foundation than a box spring (with a few exceptions for some mattresses that are typically thinner and are specifically designed to be used with a box spring. Even if you were buying an innerspring mattress though that needed a box spring though I would replace the one you have if it’s that old because a box spring or foundation is an important part of your sleeping system and your mattress needs good support underneath it with no sagging or soft spots as much as you need good support from your mattress.
You can see some suggestions here from Brooklyn Bedding (Dreamfoam’s sister company) that specifically suggest to avoid box springs for their foam mattresses. The foundation thread here also has many good foundation options in a wide range of prices that will work well for foam mattresses…
Phoenix