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.
In the Dungeon Master's Book, the book contains instructions on how to level as per this link. If you're interested in having them level all the way to thirty, you'll need to grab the book "Heroes of the Fallen Lands".
Characters created as part of the Red Box are first level characters as presented in HoFL. HoFL presents more options to the first level character though, and so players should be allowed to retrain if they wish. Beyond that, use the level progression from HoFL for your red box characters.