You can do "drip" in several large brewers, with water heated on the stove. Similarly, you could make a "cold brew" base, such as "Toddy" and add hot water. Or, buy several large French press pots. One of those methods or some combination of them is probably best.
They way you'd use cold brew is to brew a base concentrate, and store in the fridge until wanted. Once you've got the base, it's no more trouble than making instant; just dilute with hot (or iced) water, at a ratio of 2 or 3 water to each part base. Cold brew is a lot better than instant, and truly awesome for iced coffee (good for cooking too). A commercial sized "Toddy" runs around $90 and makes enough base at one time for around 8 gallons (128 8oz mugs) of regular strength coffee. Each max batch takes around 5 lbs of grounds. You'd probably brew two batches per week.
Vac Pots are great, but they're expensive.
"Army" or "Campfire" coffee -- brewing loose then straining though cheesecloth -- might be fun when you go camping, but it's wretched compared to even inexpensive but OK instant coffee like Nescafe Classico.
Using cheesecloth for a drip filter is not a good idea. Too loose, Lautrec. If you're going filter pour-over or drip, get a bunch of Chemexes or Hario Woodnecks or something. I vote Chemex because your situation sounds so sixties. A "10 cup" (50 oz) Chemex is around $40. If they were all you were using, you'd want at least four.
A 10 cup "family size" propane burning brewer runs around $100. I think there are also small commercial size (about right for you), propane fired coffee makers. Probably expensive, and I don't know who makes them.
No matter what method you choose, use good beans, store them correctly, grind the right size, and don't grind until just before using.
Hope this helps,
Edited by boar_d_laze - 7/19/12 at 6:29pm