Obviously it will be important to allow the memory foam to do what it is best for: Allowing for better contouring of your body shape and therefore less pressure placed on the areas of your body that press harder against the bed. However, don’t just go by your weight, because if you are tall, then your weight is dispersed over the bed more.
A good memory foam mattress will not need a box spring underneath it to make the mattress feel good. You can order a platform base to increase the height of the bed, but remember that this mattress should feel good if it was placed on an even, concrete surface. A good way to test the surface of a box spring or box foundation is to sit or even stand on various areas and see if it compresses underneath you. If you have an existing foundation that is weak, you can easily place two cut 3/4 to 1 inch thick plywood sheets over it to give it the necessary support.
Also, you may want to look at the warranty that a company offers, because you can then worry less about spending extra money for a higher weighted mattress and can attempt to get the correct mattress feel, but save on cost.