You need wooden pipes to draw items out of chests and machines. That's why you need them attached to the chest - so it can draw items into your pipes, much like how a transposer/filter can put items into an RP2 tube network. As for the types of pipe, cobblestone and stone pipes are for making more compact setups as they don't connect to each other, gold pipes increase the movement speed of the items (this was recently modified so you need more than one gold pipe in a row for a good speed increase) sandstone pipes won't connect to machines, iron pipes force items to go in a specific direction, diamond pipes allow you tell items to go specific directions, obsidian pipes can pick up items off of the ground, void pipes destroy items, and as mentioned above wooden pipes allow you to pull items out of inventories.
This is why I gave a quick picture and explanation above, so it would be easier for you to understand what kind of system you'd want to run so items don't pop out of your pipes. You could very well separate the two pipelines by a block and make them all the same type (except the wooden one), but it's not really needed and stone/cobblestone pipes are cheap and efficient for what you need done.
