The Timber Bear is old but has a pretty loyal following. Heavy slow, but powerful and relaible....a good firewood saw.
With regards to "sitting," remember that one of the big differences between mower/tiller engines and chainsaw engines is that the chainsaws are 2-cycle and require a gas AND oil mixture. When you let them sit, the gas evaporates leaving only the oil, which gums up the carburetor. The fix for that is that when you put them up for a long time (say, the end of the cutting season), you drain the tank and start the machine until it BEGINS to rev up (begins to run out of gas) then you shut it down. The idea is to get most of the gas out of the carb. Don't do this often or without good reason as its a bit hard on the engines...remember, the lubrication is in the fuel mix....you run out of gas, you run out of lube.
I am not that familiar with the Timber Bear, but so far I haven't seen a chainsaw that DIDN'T have a fuel filter in the tank....sounds like a recipe for rapid onset carb trouble. Filters are cheap and strongly suspect you need one.
Also, "cleaning" the carb is not always sufficient. Take the carb off, go to your local chainsaw shop and buy a carb rebuild kit. Do a search on the site regarding carb cleaning (keywords like carburetor, rebuild, membranes, welsh plugs will be helpful). The more thoroughly you rebuild the carb, the better chance you have of getting a good running saw out of it. It's easy and cheap.
Welcome to the site!! And welcome to 2-stroke engines!!