Rob, the 362 and 261 are both pro saws. The 251 you linked to is not. Just want to make sure that's clear.
The differences between the pro and homeowner lines in most lines are somewhat evident if you know what to look for. The chain-tightening system -- is it gimmicky or is it the standard one or two nuts with an adjusting screw? (Hint: gimmicks = not as reliable) The bar -- does it have a replaceable tip? Not that anyone replaces them anymore. The engine -- is it designed to be rebuilt easily? On the bigger saws -- is the air filter a flat screen or a foam-covered small automotive type filter? Look at the size of the bucking spikes, whether they're removable, and what they're made of. Is the crankcase visible and magnesium or is it hidden somewhere inside of all that plastic? Is the anti-vibe system a bunch of springs or is it rubber bushings? (Springs have started creeping into smaller pro saws, too, unfortunately.) What does the saw weigh compared to others in the lineup of the same engine size? Pro saws will nearly always, if not always, be lighter.
BTW, don't gloss over the saw's weight, especially if you don't run one every day. A heavy saw wears you out faster, and a worn-out person makes mistakes and takes shortcuts. I don't care how much of a man you think you are. I've never seen a professional arborist pick up a saw that was bigger than what they needed to do a job. The only people who enjoy running the really big saws, we're talking around and over 100cc, are pros who have other people watching them, and hobbyists. The 084's, 088's, and MS880's generally sit around and do nothing in the toolboxes of eastern arborists. They come out every now and then for huge maples and stump flush-cuts.
Back closer to the questions at hand. I've been away from the chainsaw market for a couple of years, but I've seen the Easy-Start feature you asked about break on a couple of smaller saws. If a person unfamiliar to it yanks on it like it's a regular saw, they can eventually screw up the clutch / spring / whatever system that's inside of it. And then you have nothing. I've retrofitted standard starter housings onto two Easy-Start saws for arborists. These were little non-pro MS192TC-E climbing saws that got started 50 times a day or more. Eventually they gave up the ghost.
None of the saws mentioned in this thread are hard to start with regular starters. The 362 probably even has a compression release, which is also unnecessary unless you're old and/or feeble. My 361 has a release, but starts quicker without using it.
The advice on non-ethanol and having spare chains is good. You can also buy ready-mixed fuel in sealed cans ... it's expensive but may be the best option for some. You're going to want to rotate your fuel out every so often if you keep pump gas around; not sure about the sealed stuff. Old fuel is *worse* for 2-strokes than ethanol.
One thing to be remembered is that the larger engine in a 362 is going to use correspondingly more fuel regardless of whether you're using the extra engine / bar capacity or not. This might matter in a situation where when you're out, you're out. A saw with a 16" bar is going to be good for a 32" tree ... not quickly, but it'll do it. If you have only softwoods around you and don't use your saw on any type of regular basis, I'd be tempted to err on the small engine side of the equation just for the economy concern. I've never cut Palms, so someone else is going to have to give recommendations on power requirements and how gummy they are.
Speaking of gumminess, you'll want to have some alcohol (not that kind) around if you're dealing with sappy trees like White Pines. It'll strip that sap off of both you and your saw like very little else will. Get a gallon and put it on a shelf somewhere; you can thank me later.
Forgot to add this in the above. If you have money laying around that you don't want to buy a family meal at the steakhouse with, you can invest it in a different length bar and associated chains than the one on your saw. I like to have a shorter-than-standard bar for certain of my saws (say, a 16" for the 361) which I'll put on when I need more power *or* when I know there's a chance I'll hit dirt or something embedded in the tree. Less bar length = less teeth to sharpen and less expense to replace the chain. If you want yet another bar, you can get a longer-than-standard and put a skip-tooth chain on it. This will cut slower than a regular chain but will give you additional capacity. Just take it easy on your engine with this setup. Skip-tooth chains also have less teeth to sharpen.