My first suggestion is to have a "Winter Fund" account that you save a minimum of 3 months of money in to use when work slows down. That lowers stress dramatically. When times pick up, you replenish that account before you start splurging on new toys.
Before you buy a piece of equipment, have three months worth of payments set back in the winter fund.
Get a loader of some sorts early on, a mini skid is a great asset and dramatically reduces the suck of tree work (the dealing with the debris portion).
Figure out where your debris will go and what form it needs to be in. I have it worked out where I can get rid of (essentially) infinite tree debris in whole form, meaning I don't need a chipper, which is a beautiful thing.
Find a niche, but don't be afraid to do things that utilize the same tools. For example, my niche is removals, but this year I have started doing site prep work/site contracting as well. We will also do trimming, but I usually won't personally build a fence, for example. This year I bought an excavator and track loader to do contracting work, however the excavator is fantastic for handling tree debris.
Get your name out there. (Advertise).
Starting your company right, come up with a name, handle any tax and incorporation details early on while its small, makes it easier. Find an accountant, and use their advice.