A plain way to decide before you start pricing. The job, the hours, and how long you will keep it decide most of it.
Most buyers start by pricing a new machine and work backwards. Start with the job instead.
Rent when the job is short, the machine is unusual, or you are not sure the work will keep coming. You pay for the hours you use, and the dealer carries the maintenance. Rental is also the cheapest way to try a class of machine before you buy one.
Buy used when you will run the machine steadily but not around the clock, and you have someone who can look it over. Ask what the machine did in its last life. A unit that moved snow in a parking lot is a different animal from one that ran a mulcher in the bush with the same hours on the meter.
Buy rebuilt when you want a known machine with new wear parts and a warranty from the shop that did the work. Ask what was replaced and what was only inspected, and get it in writing.
Buy new when the machine is the centre of your business, it will run full shifts, downtime costs you contracts, and you want the warranty and the telematics that come with it. The premium pays for itself in uptime or it does not. Be honest about which.
Whatever you pick, ask the dealer the same questions: what is the lead time, what does service look like in my area, what attachments are included, and what is the warranty. Then ask a second dealer the same thing. Comparing two honest answers is the whole trick.