To build up Mario's stock, try to quit stages when you are about to die. This would apply to stages like the racing stages (with the Islander who likes to race) and some of the mini-stages (like the Pachinko stage).
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If you can restart the stage easily (and quickly), you should learn to quit when Mario is in danger of dying. This will let you have a large stock of lives to tackle stages and mini-stages that you want a lot of lives to spend on (the Dead Leaf in a Dirty Brook mini-stage comes immediately to mind).