This is a post all about living in the woods biome. I think that this is one of the best biomes to start out in because it has all the basic items that you need on a day to day basis. Because you get the wood you need from the trees. You get food from apples that fall from leaf blocks. And you could make a home in the ground or a little plank home on the ground.
I think that the best place to make your home is near a water source. Then when you are ready to farm you can just make a farm next to the water instead of going and finding water and maybe getting lost on the way.
I like to make a small house above ground to help me find it. But I put a majority of my rooms on a staircase that is going down from my main room. I try to make as many rooms of my central staircase as possible because you can get a lot of cobblestone and precious material just from mining out all the rooms on a stair case.
I suggest that you try to find out what kind of forest you are in when you first spawn. Because if you are in a roofed forest where nearly every thing is covered by trees you better make a sword because that means that a lot of monsters might spawn and not burn up because there is enough shade. Or if you are in the jungle you should start looking for cacao seeds which are a very good resource.
I hope that this is helpful and informative and you want to be making your little house in the Minecraft woods.