Generally the best mattress for side sleepers is a pillow top, latex or memory foam mattress that is medium firm.
However be aware that is just the general rule, ultimately it all comes down to your weight and body shape.
Being a side sleeper you fit into the most common category. More people sleep on their side than on their stomach or their back. However sleeping on your side creates an opportunity for your spine to get quite far out of alignment.
The aim of getting the right mattress for your sleep type is to ensure that the spine is kept neutral throughout the night so you do not wake up with any aches or pains or develop a bad back over time.
Your shoulders and hips are the heaviest parts of your body, therefore there needs to be some give in order to allow them to sink lower and ensure the spine is kept neutral.
If a mattress is too firm and the hips and shoulders cannot sink in a little the spine will be forced to arch unnaturally to compensate. Likewise if the mattress is too soft the hips and shoulders will sink too far and cause an overextension.
The answer lies in a medium-firm mattress. The idea here is that there is a firm layer of support on the bottom with a medium layer on top for comfort. This gives you the support your back needs but with a bit of give on the top to allow the body to fall into that natural alignment with a neutral spine.
How far to the firm side you go or how far to the medium side depends on your body weight and body shape. If you are lighter you need less give and can tend towards a firmer mattress, if you are heavier you need more and can tend towards medium.
In addition you also need a higher pillow to keep your spine aligned. Because you are resting on your shoulder your head is higher off the bed so needs extra support.
The best type of mattress to offer you this kind of support is a memory foam or latex mattress. In particular a company that lets you customize your level of firmness is the best. Green Sleep and Savvy Rest are two examples of latex mattress manufacturers that allow you to handpick the firmness level of each layer in the mattress.
If you are going for the traditional innerspring mattress look for one with a pillow top. The pillow top is a softer comfort layer that is put on the top of the mattress. If you get something that is firm with a pillow top you are replicating that medium firm effect.