I've used chainsaws for many years now and have been on the appropriate training courses so I feel qualified to comment on this thread.
Whatever you do, don't lift your saw up to shoulder level to cut a tree or anything else for that matter. That just happens to be where your neck and head are.
If that chain touches you, it won't be a nice clean cut that a couple of stitches will fix.
Cut the tree at the bottom, then it's only one cut. Have a look on the internet to see how the experts do it. Wear proper safety gear, chainsaw legging have Kevlar in them to clog up the chain so that it stops quickly therefore minimising the damage to you.
I've used many makes of "professional" saws but the one I use for use in my garden, is a McCulloch 838 with a 14" blade, I've had it for 15 years and it's done a lot of work. It's easy to work on and parts are readily available and cheap. A 14" blade will be plenty long enough to cut what you've got. Remember that you've got to carry it around all day and you don't want to be carry around excess weight, it's tiring. Anything more that 14" would be like taking a sledgehammer to crack a nut.
I won't recommend any particular brand, that's a matter of personal preference and budget.
If you have any specific questions, I'll try to help.
