The idea of treasure in 4e is simple: the DM has a list of stuff and money that you should get that level.
The consequence of this idea is non-trivial, as it leads to quantum treasure. If you carefully loot all of the random "trash" from monsters, pry out the iron nails of the doors, and otherwise find enough stuff to load up a cart and haul it back to town: you'll get the value of x treasure parcels, depending on how generous the DM is feeling.
If you fail to loot bodies for "trash" items and only carefully take obvious magic items and other "treasure" ... you'll end up with the same amount of gold at the end of the level *. In the Gygaxian sense, encumberance is just there to threaten the players with if they are hauling around ovbiously too much stuff without appropriate hauling mechanisms.
From Carrying, Lifting and Dragging:
Adventurers carry a lot of gear. When that quantity becomes extreme, it might be enough to slow you
down and otherwise hamper your capabilities. The amount you carry should rarely be an issue, and you don’t need to calculate the weight your character is hauling around unless it’s likely to matter.
To figure out how much of the dungeon furnishings you can carry around before taking penalties, use (as stated in the above link) strength * 10 in pounds. (A completely unrealistic number, BTW). exceeding that will slow you down by some amount. You can barely lift strength * 20 pounds, but then you're moving at best 2 squares per move action (you have the slowed condition.)
Looting, therefore, should only be done if the players actively enjoy counting rivets. (I sometimes actually do, though it tends not to be in games like 4e). At first level, grabbing items off of fallen enemies is actually kind of neat, though it very quickly becomes irrelevant when you have your own, magic, items. If a player wants to obsessively loot, let him or her, ask them to describe how they're storing the stuff not on their person, and treat it like a treasure parcel that has to be redeemed at the local blacksmith.
If the person wants "full value" for the iron bands, rivets, broken doors, and daggers that they collect, they are welcome to sell them at 20% to anyone who wants to buy, and have that value deducted from a future treasure parcel.
If you're interested in other treasure-abstractions, take a look at Penniless but not powerless 1 and penniless but not powerless 2 which explore a further level of abstraction (quite welcome, IMO) for 4e.
What your group should do is ask the DM, in advance, for the kind of awesome treasure that they want. The idea of wishlists is quite handy for the players and the DM and saves time all around. Then just don't think about the coincidence of finding the exact magic item you asked for, it breaks suspension of disbelief. :)
*This statement is less true for redbox, as treasure is randomly determined, but the idea remains the same, as the GM should treat the "load of trash" as a plot coupon for a treasure parcel. Quantum-treasure works, so long as you don't think of it like a simulation.
Well, for starters, I'd say don't use D&D. It is a game tailored towards violent conflicts, which is exactly what you're avoiding, it seems. Mind you, I said "violent conflicts". No story, thus no game, can exist without any conflict whatsoever. I'm not also saying it's completely undoable with D&D, just mainly... a waste of its design and practical goals. Another way to put it, to use a metaphor, is: smartphones are great, you can do a lot with them, they're like handheld computers... But they can't really substitute a desktop computer in every way, maybe not even most ways.
Now, if you're willing to work outside of D&D, there are some good systems out there for that "action and adventure doesn't mean swinging swords all the time" vibe you're after, like, for example, Fate (The Dresden Files RPG, Spirit of the Century, Diaspora, etc), in which most of the mechanics about resolving conflicts are the same, regardless if it's a brawl, a wardrobe and style show off or even an economic dispute between Lex Luthor and Bruce Wayne. It's worth a look, really, and there are SRDs available for some of those games (Spirit of the Century and Diaspora, iirc).
If you're sticking to D&D, plotting the campaign isn't the difficult part; the difficult part is to design encounters (which is just a way of saying "conflict scene") that allow your PCs to shine doing their thing when most of their sheets are geared towards combat (yeah, players do that, it being the game it is).
For the wizard (most hocus-pocus folks, really) and rogue, that's easy. Most other types, though, will rely purely on RP, most of the time, which isn't bad per se, just kinda unfair, since some players get to look at their sheets and say "I can do this, this and that", while the fighter's player has to memorize lines from Gladiator and the ranger's player has to become a living Bear Grylls encyclopedia.
If your group can pull it off, that campaign'd be the stuff of legends, but it'll be hard, really.
Best Answer
It is apparent that you are facing multiple issues here. I will try to address them individually. But first:
Get everyone on the same page
You all evidently have different expectations of play, the game has a few levels of agreement that have to be acceptable to all players, the social contract, and choice of game, and the story of the game are just three examples.
You can use The Same Page Tool - It can help your group discuss and define what you are expecting to get out of the game, an excerpt from the link:
After you have figured out what your expectations are - you can start thinking about what world to play your game in. There are a few options available to make it so that anyone could GM those worlds.
1. Choose a world you all know.
Choosing a world you all know (like Middle Earth, or Narnia, or even a historical period) is pretty straightforward, but you should make sure that everyone has about the same level of knowledge about that world, or that it is easily accessible.
2. Create a world together.
You can do this on your own - or you can use a cool minigame designed just for this like Dawn of Worlds which puts everyone in the role of a god-like creator taking turns designing and building a world and giving it a basic history, excerpt:
Once you have that - the decision of who will be the GM is something that I can propose two methods for, but I am sure others exist.
1. Choose a GM each session, and every player also has a PC
In this manner, the GM role is a "hot seat" players taking turns playing the GM and their own characters the rest of the time. This is a bit tricky if you are doing long campaigns, but for sessions of a few hours with smaller adventures this could be really fun.
2. Take turns running adventures in the same story
Every GM will play out their adventures and then switch out with another player at the end. You could also keep the PC's stories perpetual, just switching out one character and adding another they might meet on their travels - this keeps the players vested in their characters and also provides for some interesting stories.