I spent many years fixing saws including dealerships for both Husqvarna and Stihl. A good quality saw with a properly sharpened chain makes a huge difference in the ability to cut wood.
mbopp makes a good point about safety gear. I was removing a tree at home at a time where I worked for a joint Husky/Stihl dealer. I made an improper cut that I should have known better while not wearing safety pants (that I could have purchased for slightly over cost). I was really lucky that I only ended up with 19 stitches on my right knee, which still gives me problems 6 years later. Even a cheap saws with a dull safety chain will go through flesh pretty easily.
If you want some good chains (professional) that will cut chips instead of sawdust, try www.baileysonline.com. Be warned that most of the chains do not have the anti kickback feature used in homeowner type chains! They cut, and very well, but will kick back and hurt you very badly if you are not attentive and know what you are doing. They also sell safety equipment and repair parts etc.
Good luck, safe travels and SAFE CUTTING!
I've been extremely happy with my Stihl 180 CB-E. I didn't care much for the chain that came with it, so I use Oregon chains (not safety) and 14" bar instead. It's small (just 32cc) but still has plenty of power.
I'm not interested in braining myself should it kick, so have a helmet with face shield and earmuffs. I also wear a thick denim coat and chaps.
Now if only all trees would fall the way I want them to, and not the way they actually lean...