It all depends on how often you want to clean the coop. If you use the linoleum/tile floor, you will have to clean a lot more often. If you use the deep litter method directly on the ground, then cleaning won't need to be done as often. Plus, the DLM will react with the moisture in the dirt and provide fantastic natural compost for your garden (assuming you have one). If you go with DLM, just make sure you make the opening of the pop door about 3 -4 inches off the ground. That will keep the litter from spilling out.
Another way to trap the shavings/litter is to put a board in front of the coop door - but you will need to compensate by having a taller door. My coop door is raised from the floor by about 5 inches so they have to hop up and then walk down the ramp. It helps keep the litter inside and the door from being able to be pushed up/open by predators.
I use vinyl over the wood flooring and put 4" of pine shavings with DE down. Then I will refresh it with a new top layer of pine shavings as needed. Then when I need to do it I simple scoop it all out and replace. I've replaced it all 2 times now - once in preparation for fall and now for winter. I suppose I could leave it longer - but I don't like poop in my shavings and we still had a few that weren't using the manure box/roost so they kept leaving piles on the floor. Now my chicks are using the manure box so there are less droppings on the floor.
In this picture you can just about see the 2x4 I have in the doorway on the left to trap the shavings.
We got a small scrap of linoleum (left-over/scrap material) and glued it down to the plywood floor. Then put down pine shaving bedding, maybe 3 inches. Change as needed. Its easy to clean out and we've had no problems, even with wet northwest winters. Small bits of material are easy to come by and can easily be cut to fit.