I need to buy a new mattress for my slatted king size bed.

Hi Ingrid, 
 
Thanks for your question. 
 
At your body weights you would be matched with a Medium spring tension to get the right level of support;
 

 
However, you are borderline between a Soft and Medium spring. For a bit more give choose the Soft. For a bit more supportive feel choose the Medium spring. 
 
The only restriction is from yourself being a side sleeper. Side sleepers need to avoid anything too firm in the top layers as this will simply cause pressure point pains in places such as shoulders, hips and knees. Back sleepers aren't really restricted. 
 
Have a look at medium feeling models in the comfort layers such as our Origins Pocket 1500 or Artisan Naturals. The predominant difference here is that the Artisan range is constructed from natural fillings and not only do they last longer as standard but also give a cool sleep surface. 
 
Both of these models in a Zip and Link option are fine to be used with a slatted base as long as the gaps are no bigger than 3". If they are then you would simply need to place some standard sheets of MDF, plywood or pegboard. 
 

 
If the base is sprung slatted then you may want to board the base straight away to prevent a ridge from forming in the middle where the mattress attempts to conform to the dip. 

I hope this helps but if you have any further queries please don't hesitate to contact our office on 0161 437 4419.
 
Kind Regards, Lee.