I personally like to make a few wooden axes and have extra wood to whittle away at during the first night - a workbench, fences, stairs, some tools, signs, ladders, torches if you can, etc. I can get about 2.5 stacks of logs with 5 wooden axes before sunset. That comes out to about 10 stacks of 64 planks.
My most recent game (an hour ago) I spent my first night in a tree after building a ladder up to the top (punch through the leaves and branches to expose the trunk, then add ladders to it). From there I made a platform up there out of planks and finally a bridge to the nearest cliff face to start mining. It's helpful to take a minute or two and search for nearby caves, as they have some sort of coal deposit in them about 2/3 of the time.
A lot of people apparently opt to carve out a small cave, block it off except for a 1x1 hole to the outside and start exploratory mining immedately - this is also a solid option as long as you have torches for light so the cave doesn't start spawning hostiles on you. Make some Stone picks to make the time go by quicker.
I was able to start playing immediately when I bought the Alpha, and it should do the same for you as long as the servers are up.
Once you connect, you can play offline if the servers go down.
They do say it can take an hour to process your order. Mine went through in seconds and I could log in and play.
Being prepared is playing. It's hard to describe what will happen to you as that really depends on what you do.
Tips for survival?
- Be very careful about being out in the open at night. Hostile creatures can spawn in the open at night and any time underground where there is no or little light. These include creepers (which will sizzle and explode when they get close but are otherwise silent), spiders (which are 2 wide and 1 tall, make chittering sounds, and love to jump attack you), zombies (which moan when not chasing you), and skeletons (which fire arrows at you and make clattering sounds).
- Light your way underground so you can find your way back and prevent hostile spawns from coming at you constantly.
- Don't dig straight up or straight down. Digging straight up can result in being crushed by piles of sand or gravel. Digging straight down can result in you being dropped into a cavern or pool of lava and dying. When digging down or up, always dig the space in front of you (or several spaces in front of you if you might be near lava flows). Make a set of stairs to your destination.
- You can suffocate under water, and in water you only do about 1/2 your normal damage to blocks and creatures.
Look up some construction guides or check the Minecraft Wiki (Google can help find it) for recipes on crafting if you want to know what you can make.
Well you just create your account, download the game, pay.. and then it'll either be instant-ish or it'll take awhile because of other people buying the game. I love this series so I think you should go watch a few episodes to help you not get eaten by zombies & spiders :3.