Rafts are much easier to build than even the simplest of boats, but tend to be slow in the water and difficult to transport.
A basic raft can be built out of shipping pallets or plywood, but either method severly restricts your transportation options.
>> View photos of my barrel raft
I have seen a number of designs which use logs and barrels, and in this case, you can just transport your barrels riverside. It will be much easier to lash the barrells with 1" webbing instead of inexpensive rope.
If you are looking for something that will last for a long time and is a bit speedier in the water, you should look into buying some marine dock foam. It tends to be pretty expensive, but it can be easily shaped and is reasonably durable. The cheaper 2" insulation sheets available at Home depot, lowes, etc are not as sturdy.
Raft Building Tips>
Regardless of your material I recommend going with a catamaran type design, and making the length of your craft 2x the width. A raft with a longer waterline will be faster.