I've tried pressing ginger in an Italian cast aluminum garlic press. It didn't work- squeezed some juice out, nothing more.
I've got a mini food processor that works well for larger amounts and I've also made up batches of ginger paste in the blender and frozen it in cubes.
I've tried mincing ginger with a chef's knife and I can't say I'm much of fan. I like my ginger completely pulverized- something that takes patience to achieve with a chefs knife.
My favorite way of working with ginger is to make an infusion with it. I take whatever liquid is in the recipe, add a few pieces of roughly sliced ginger, bring it to a boil in the microwave and then set it aside to steep a few minutes while I do something else. I strain/use the liquid and toss the ginger pieces. It's not the most economical approach as the pieces still have a lot of flavor in them, but as long as I get my ginger for $1.29/lb at my Indian grocer, the method isn't breaking my bank.
I have also given some thought to the difference in taste between a boiled ginger infusion and sauteed minced ginger... and, I'm not sure that the difference is that substantial. A sauteed onion and a boiled onion are a night and day difference in flavor, but boiled and sauteed ginger... eh... I'm really not so sure.
I feel pretty comfortable boiling ginger. And, for that matter, I've also pretty much stopped sauteeing garlic as well.