Don’t sell your magic items, just break them down. This goes hand-in-hand with number 1. The randomness of the crafting magic means that I created plenty of items with stats that were of little use to me. My monk didn’t need strength or intelligence. So I had to craft several of the same item before I got one with stats that were useful. The more crafting materials you have, the better.
Make sure all of your followers are properly equipped. They have slots for two weapons (one if two handed), a necklace, two rings and a focus. Although the damage they do is considerably less what I did, the little pokes and stabs they do means less damage you have to do. Giving them gear that increases their damage or healing could be the difference in a kill or a long walk back. Your followers also never die, they just rest and won’t fight for a time before rejoining your side.
Watch for visual cues in boss fights or when exploring. As in World of Warcraft, certain fights will offer visual cues before special attacks. Later in the game, environmental obstacles that can damage you will do the same thing. An area of the floor will glow or swirl, an item will drop on the ground that appear innocuous at first but will explode a second or two later. If you played WoW, you may recognize a few boss fights in Diablo 3. That is not a bad thing for survivability.
Utilize checkpoints as often as possible. There is no save in the game. The game is saved on Blizzard servers at checkpoints, when entering a new level or using a way point. An unexpected disconnect could lose your progress and force a regeneration of the random map or dungeon.
Don’t assume Nightmare difficulty is just Normal mode with harder hitting mobs that have more hit points. My entry into Nightmare has shown Elite and Champion mobs with new attacks and AoE, forcing me to move more or run around a bit to wait for an ability on cool down. These fights can be tougher than the boss fights. Also, I find that I am utilizing the environment to put obstacles in between myself and certain types of mobs. Nightmare has its name for a reason, so be warned.
I am just beyond the Skeleton King and working toward the Act I conclusion. That last boss will be a true test of just how ramped up Nightmare level is. Hopefully, these tips will help you get there so we try some co-op together.