If I get new kitchen cabinets and linoleum flooring and a new dishwasher should I put the linoleum under the cabinets and dishwasher first.
This is mostly a personal choice. With linoleum, the only difference would be in spending the extra money on additional materials to put it under the dishwasher versus just far enough to look good. I recommend doing the countertops before the linoleum only because gravity pulls dirt down - why have the countertop people mess up a brand new floor when you can have the floor go in later? If it were hardwood or tile, I would recommend putting the floor in first, all the way under the cabinets, to make sure of clearance heights under the countertop for the dishwasher, but linoleum is thin enough you don't have to worry about that.
The general rule is that anything permanent or structural should be built into the sub floor and the floor built around it. Anything temporary or unattached, like a dishwasher, should go on top of the floor.
For cabinets it depends how they are mounted. Base cabinets are usually mounted to the wall, but their bottom framing is usually meant to be flush against the floor, so it could be argued that they are "part of" the floor, even though they are not. For this reason, they should really have their own special floor surface, and the human floor (the linoleum) should go around them.
If I were to install base cabinets, I would probably first level and nail a plywood base to the floorboards that would be mated to the cabinets. The advantage of this is that it would make a perfectly flat platform to work from. You don't want to just assume the subfloor is flat. Also, I can seal off the plywood or add a pan or membrane to make it waterproof. For example, lets say the sink leaks. Where will the water go? You want to know the answer to that question. Having a nice, tight plywood base also prevents any possibility of a small crack or hole that a mouse or spider could travel through.
So, short answer: linoleum under dishwasher, around cabinets.