Ok, I really don't know. We're actually going to add gutters to our house because I want to do this. However, its only going to cost us about $75 to add gutters. Our roofline is odd, and we only need 60 ft of straight gutter system with end caps.
I mean... maybe if you find one good line of roof and just add gutters there to extend to your rain barrel, you wouldn't have to do the whole roof? Lowe's has the gutter systems pretty cheap.
I agree, maybe just add gutters to one side of your roof -- the side with the most surface area. It will vastly improve the volume of water you could potentially collect passively.
Describe how your roof system looks: i.e. does it have valleys? or is it simply sloped to the edges of the roof system? do you have water diverters over entryways? single story house?
You can also use ground level gutters, altho' perhaps not as efficiently.
My house has a difficult roof line along the West side. Unfortunately, the basement wall can get very wet there, especially during snow melt days.
One way I dealt with this was to dig a shallow ditch at the drip-line and install a regular plastic rain gutter section. I placed boards on either side to backfill the soil against and to hold a row of bricks laying on top. The bricks are the ones with holes in them.
At the downhill end of the gutter section, I dug a large hole. This 3 foot deep/2 foot diameter hole was filled with large rocks and covered it with soil and sod.
I'm sure that there's a fair amount of water that splashes off the bricks but at least it doesn't end up on my basement floor these days. My yard slopes enuf that I've actually considered allowing the gutter to feed into a small pond at the corner of the deck. That would be about a 50' run of gutter is all and it is sufficiently downhill that the "pond" could be whiskey barrels a little above the soil-line.
A whiskey barrel pond here wouldn't work very well as a growing season reservoir, however. We have gotten as little as 1 inch of rain during the entire 3 months of Summer, some years. But, I'd still need a big hole with rocks in it under the barrels to handle snow runoff .
Your roof looks somewhat symmetrical, in terms of area on the front vs. on the back . . . so if I were you I would think about where you would want to place the rain barrel (on the backside, probably) and set up gutters there. Your terrain looks flat to me, so I don't think you could easily hook up a "ground gutter system" (or trench) easily to let it gravity-feed a rain barrel.
Ok. Hipped roof over the garage with 1 valley on the back of the house (maybe? should be). You could put a barrel where it would collect the water from that valley on the back of the house. The front as well should you be so inclined. Of course the barrel would have to be open. Maybe a top you could remove and replace as necessary. It won't collect nearly as much as a gutter system would, but some is better than none. Hope this helps.