Well, Florin, you're going to want to plan on gear that can take some wet weather. That's not the peak wet season there, but it is a wet season. You likely can expect lots of clouds and fog, and a good chance of rain.
So, for boots, something that will keep you dry and warm. One good choice would be the Lowa Valojet GTX mountaineering boot ($350). These are tough, fairly light boots with uppers of synthetic leather and Cordura, so they wear well and resist moisture. Gore-Tex liners provide a final barrier to wetness. They're pretty good on the trail, and up to most any mountaineering challenge. Asolo's Expert GV boots ($310) would be another good choice—uppers of waterproof Perwanger leather and polyamide fabric, Gore-Tex liners, good cushioning, and gripy outsoles. Fine for the trail, and good for snow and ice as well.
For a sleeping bag, something rated to around 0 degrees F is the best choice. Marmot's Never Summer ($269) meets that spec in a down-filled bag that weighs a bit under four pounds. It has a water-repellent finish to help keep it dry. But moisture still could be an issue. So you might consider a synthetic bag, such as Mountain Hardwear's Lamina +0 ($195). Weighs a little more than a down bag (4 pounds 12 ounces), but if there's a good soaking it will serve you better.
Take a waterproof ground cloth (plastic sheeting is fine). And maybe a vapor barrier liner like RBH Designs' VBL Liner ($100). The VBL gives you lightweight (five ounces) insurance in case temps drop below zero on the upper reaches of the mountain. Which is a distinct possibility.
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