Cif (used to be Jif) is the best thing I ever found for cleaning cookers, but I've never used it on stainless steel. Once the grime is off, use a little baby oil on a piece of kitchen roll to get the steel to come up smear-free.
I just use hot soapy water (washing up liquid) on my stainless steel cooker top and buff to a shine with a microfibre cloth. You should be able to buy these cloths in most supermarkets.