Hi Ashley,
Use the chips form the removal for wine caps, and the logs for shitake. If the trees are of decent size, I'm guessing you'll have
enough logs for other types of culinary mushrooms as well.
Regarding renting or buying a wood chipper, will depend on your ability to properly maintain the chipper. It also depends on your budget to buy verses rent. You can rent a professional grade chipper, for several days with your proposed budget, which could yeild over 60 yards of chips in professional settings with the crew and wood to efficiently
feed it. Any chipper you would buy for that same price most likely wouldn’t be of professional quality grade, or in good condition, though you might find one that goes on your
tractor pto, and works ok. So knowibg the size material you need to chip, and shopping around is the best answer to your question.
The feed intake which determines the size wood or brush you can efficiently chip, will let you know if it will be efficient to use for your circumstances. The biger the feed intake the less work to prepare material for chipping. From a professional standpoint, small feed intakes aren't worth it, unless your only dealing with small uniform material. So looking at the wood, brush and braches you have; then the work you must do to make them small and unifomed, plus the extra effort to feed all those smaller peices individually, will give you an idea of the efficiency based on your smaller feed intake. Even with a 3" feed intake, a 1 inch twisted branch can get hung up easily, plus any lateral limbs coming off the branch, create resistance that can make feeding impossible with out stripping the branch. In tree service work, the most sought after are large professional grade chippers that will take a 15-16" log whole, or a 12 inch tree whole, with minimal processing to reduce feed jams.
Chippers require proper machining to sharpen the blades while keeping them in balance. The blades also need replaced after so many sharpenings. The bed knife needs adjusted to spec, as your knifes get machined down after sharpening. They also need greased and properly maintaing like any piece of machinery. So how often you plan on using the chipper, the material you plan on chipping, the cost of maintenence, what type of chipper you can afford, and how much work you're willing to do prepping material to chip, will all be factors you must quantify, to determine what will be right for your situation.
Hope that helps! Best wishes!