I do a bit of storm damage cleanup with a couple of different volunteer groups. We usually try to have both 50cc saws (eg. STIHL MS261) with 16 - 18 inch bars, and 70cc saws (e.g. STIHL MS461) with 25 inch bars to cover most of the wood we cut*. Some of the groups also have larger saws (e.g MS660 with 36 inch bars) for larger trees, but you always have to draw a line on what it is that you cut, and what you leave behind for others. The size of the equipment you choose helps to define, and remind you of, that.t takes forever to cut trees (20-30"). I use the saw for storm cleanup.
I mentioned STIHL models, but Husqvarna, Dolmar, ECHO, whatever, applies as well. The larger saws help to pull a longer bar, but also provide more power, and a offer bit more reach in cleanup tasks. The smaller saws let you limb, and cut a majority of the smaller trunks, etc., without the additional fatigue of carrying a heavier saw all day. Good to have a mix, as well as multiple saws to cover breakdowns, free pinched bars, etc.
*I also really like having a powered pole pruner for storm damage work, by the way - it helps me reach horizontally to test and relieve tension and compression from a safe distance without having to wade in among a bunch of branches which may shift and trap me. It also lets me 'simplify' a fallen mess, by removing all of the smaller limbs first, even up high, so that I am left with just the main trunks bearing weight to figure out.
As far as the chain, I encourage folks to use semi-chisel chain for storm damage cleanup. Tornadoes and hurricanes tend to throw a lot of dirt and crud into the bark, and the downed trees are often mixed in with debris (glass, roofing material, metal, flying cows . . . ) that are hard on chains. Much of it is near the ground or in the mud. Semi chisel holds up a bit better in this use. And since the work is deliberate (make a cut - see what moves) versus production cutting, the slight loss in cutting speed is usually not an issue. Skip chain might be something to try on longer bars (24+") to help clear chips. If you are using it because your powerhead bogs down, it suggests that you really ought to have a more powerful saw for that length bar or that type of task. A simple, fairly inexpensive idea is to buy one, and try it side-by-side with your current chains to test the difference on your saw and the work that you do.
As the comments above note - a sharp chain rules all. Storm damage is hard on chain, so it helps to carry a few chains for each saw, to swap out if damaged or dull, as well as a way to do basic touch-up sharpening in the field.
Philbert