Starting from the head and working down-
Logging helmet system w/ hat / screen / muffs - The screen keeps chips out of your face as well as your eyes, though you should still also wear eye protection of some sort. I tried doing a few combinations of separate screen plus muffs, and it was a problem getting all the stuff on and to stay in place while cutting. Tried a combo muff/screen setup, and that was better, but still didn't really want to stay on right, the weight of the screen kept trying to turn the muffs on my ears. With the hat, the harness holds everything in place much better. I have a Husky setup, but don't see a lot of differences between them. The only thing I would do differently is look for a hat with a knob adjustable harness rather than the locking tab style - it is a PITA to adjust the tab style, and if you want to cut in the cold and wear a ski cap under it, or a sweat band in the heat that can be a nusiance, or if you want to loan the helmet to someone else. With the knob it is much easier to make the hat fit.
Some folks wear the various styles of chain saw shirts - I haven't seen the evidence that they provide enough added protection to be worth the money, however a good snug fitting long sleeve shirt is worth while.
Gloves - For use with the saw, I wear a pair of LumberWorks chainsaw gloves, that I purchased through Amicks - I think they are one of the best chainsaw gloves you can get in the US - I did a lot of looking and hadn't found any others that met my standards. I have a pair of the Husky chainsaw gloves, and they are very poor in comparison - less padding, don't fit as well, and the open gauntlet style serves to collect chips and funnel them down to the fingers where they get you under the nails when you put the gloves on.... The Lumberworks gloves are a "technical" style form fitting glove, with more saw stop padding (Listed to the EU's highest standard, the Husky's are the lowest) and vibration absorbing gel pads in the palms and fingers. They also have a velcro closure at the top that keeps the chips out pretty well. However they are kind of pricey, so I don't like wearing them unless I'm actually using the saw. For handling wood I wear the rubber coated stretch fabric type gloves such as made by Showa/Atlas glove (best durability of the brands I've tried) - at the hardware store they are around $5-6 / pair, but I get them in bulk from Cooper Safety Supply for less than half that. (Last time I got some it was around $70 for four dozen pairs, add a bandana to the order and I got over the minimum for free shipping)
Chaps - I've heard Labonvilles are nice, but you need to be careful ordering as they have a different sizing method, so if you order by your usual pants size they are too short. However I ended up with a pair of Stihl pros thanks to a sale at the local hardware store... They are nice, but I don't see anything about them that would make me think they were signifcantly better or worse than any of the other pro-grade brands. One thing to mention though, is that you need to read and follow the washing and care instructions on the chaps - they do need to be laundered regularly to keep the pads from matting down, but it is important to use the right stuff to wash them with, as some products, such as bleach, can destroy their protective properties.
Boots - Steel toes are better than nothing, but they don't offer much protection to anything but your toe area, and supposedly the accident studies show a lot of hits to the top and sides of the feet as well... You are going to get a lot better protection by wearing a pair of chainsaw specific boots. These have padding built in like chaps, and protect more of your feet (plus they have the steel toe to protect you against dropped rounds) I've seen some EU brands that look like rubber boots, and I have to wonder how comfortable they are, but their cost is fairly low. Labonvill also carries a line of chainsaw boots that look pretty good. However what I wear are Matterhorn Chainsaw boots - they are quite expensive, but I've never had a pair of boots that are as comfortable, and they are built to last, so aren't a bad investment - plus they offer more protection and a better feature set than any of the other boots I found on the market.
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