Use your sneak skill when entering any new biome and listen carefully. Everything makes some kind of noise. Once you know what those sounds mean, you can either avoid or hunt whatever it is. Don't walk around like you own the place until you've set yourself up in that biome's gear.

As for meadows vs dark forest, you should be wearing deer armor, have a crude bow, a shield and a flint weapon. Your weapon has a combo attack with the third hit dealing more damage. Dogding and moving around works for the greys and it will work for you too, and if you use the small shield at the last possible instant, it will give you a bonus. Or, use the tower shield if you aren't sure about getting the timing exactly right. Put it away when you don't need it because it will drastically slow you down. That's usually enough to take down a normal grey. Try to take them out before their buddies arrive. Run away from anything else until you can upgrade. Stay away from the pink clouds and the large caves for now.

Your goal is to get your armor rating at least to 10, and then carefully raid a crypt. You will need to bash some skeletons to upgrade the deer armor first. Clubs work better on skeletons than other weapons, but they will fall to the third hit whichever one you use, as long as they aren't starred. Use your shield and hide behind trees for the archers. The giant blue guys make great starter armor, but killing them is a more advanced skill. Take advantage of your bow, the terrain, and even your pick ax to stall them long enough for the bow to work.

And always beware of the trees.