You need to be a little careful with using regular window screen material. The first issue is air flow. The mesh is close enough that air flow is actually diminished to the point that your burners will need to be adjusted for proper air/fuel mixture. If you use the fiberglass type, be aware that it will melt from the heat exhaust of the furnace definitely and probably the WH. If you use the metal type, it will rust quite quickly due to the increase galvanic action of the applied exhaust heat.
I've never considered the outside stainless steel screens to be ugly, but, I guess like all other things it is a personal decision. They've been around for years, are manufactured so that the mesh is small enough to do the required job, but, large enough not to affect air flow. Are external so that they can be replaced and cleaned if they get dirty. I think I had one that had just started to rust (again, it was on the hottest exhaust port; the furnace), but, that was after well over 5 years. I got my value for the money and even then it didn't look bad and I never replaced it (traded that trailer in on a new one). We live in the country and have lots of wasps of all kinds, wolf spiders galore, and a host of other "creepy crawlies" and the, tried and true, commercial, external SS screens do their job...now if mice were only that easy...
My 2 cents, your mileage may vary...
2 Cats; J-Lo and Ragamuffin :R
2014 Thor Tuscany 40RX DP
2011 Ram 2500 Longhorn CTD HO
2011 Keystone Cougar 318SAB (now gone)
2008 FunFinder X 210WBS (Sadly gone)