Terraria

TL;DR

Play whichever platform/version is most convenient.
Normal/Softcore/Classic difficulty, use the Guide's help, make extra NPC houses.
The official wiki is very helpful.

Different versions of the game differ slightly, but mostly in regards to unique crossover items and ultra late-game content. Play whichever is most convenient for you.
Start with a world at Normal difficulty, in Classic/Softcore. Higher difficulties, etc. are for veterans and people who play in large groups.
- Alternatively, Journey mode is roughly Terraria's equivalent of Minecraft's Creative Mode, but note that Journey characters are locked into Journey worlds (and vice-versa).
- 'Hardmode' refers to a change that happens in the world after killing a certain boss, not a difficulty.
Small if you're playing solo, Medium if you're playing with a small group or really, really like exploring. Large is *absurdly* big.
Corruption or Crimson are mostly equivalent. The biggest change is if you want your world's evil biome to be purple or red.
- If you really can't decide, Crimson world gear is slightly better at the cost of the enemies being slightly stronger.
There are some variant ores also chosen at worldgen. (Tin instead of Copper, Lead instead of Iron, etc.) They're identical in every way that matters.

The very first thing you should do is start chopping down trees to get wood. Make yourself a workbench, then create some background walls and a door for a house.
If you kill Slimes you'll get Gel, which can combine with wood to make Torches, the game's primary lighting source.
Combine stone and torches to make a furnace, this is where you smelt glass and metal.
Listen to what the Guide has to say. If you select "Crafting" when you talk to him and drag a Material item into the blank slot, he'll show you everything you can make with that item plus the other required materials and where you make it.
- He doesn't differentiate between "you can make it right now" and "requires drops from the final boss", so don't worry if it seems like a lot.
Don't eat regular mushrooms! Make bottles (Sand -> Glass - > Bottle at a furnace), place one on top of your work bench, and you can use them to brew potions.
When night falls, start digging or spelunking. It's a good time to get underground and look for ore.

On your inventory screen, there is a house icon in the upper-right section of the screen, next to the PVP toggle and the team colors. Click on it to get options for assigning NPCs to certain rooms and determining if a room meets the requirements for housing NPCs.
An NPC house needs a chair, a table, a light source, a door, and a non-dirt background wall. Work benches count as tables.
Try to always have an empty house or two, new NPCs will spawn as soon as you meet the requirements, which you can and will do unexpectedly.
NPCs don't care about the quality of their house, but they do care about what biome they live in and who their neighbors are. Happy NPCs charge less, unhappy ones charge more.
Don't cram too many NPCs into too small an area, it tanks happiness *very* quickly.
It can be worth looking up how to maximize happiness, as can save a ton of money over the course of a game, and unlocks biome beacons, the fast travel system.

When you're underwater, don't forget to breathe. It's very easy to accidentally kill yourself by not noticing when you've run out of air.
Chests often have really cool stuff, don't neglect searching caves for them. This is also where you'll find Heart Crystals, which increase your max HP.
Once you're strong enough to tear through zombies and demon eyes, you can start exploring at night. Fallen Stars can be combined into Mana Crystals, which increase your max MP.
Get a piggy bank from the Merchant as soon as you can afford one, and carry it with you everywhere. It keeps your money safe, and provides 40 inventory slots for the price of one.
- Every piggy bank on every world links to the same 40 slots. This is useful for transferring things between servers and giving yourself access to certain items from anywhere, but it also means that carrying 100 pigs will give you no more inventory space than 1.
Don't be ashamed of "wasting" resources like metal on potions/furniture. Even a Small world has more stuff in it than a single player will probably ever use, and Gold equipment gets outclassed very quickly.
Save fishing for once you've found the Angler at the beach and can pursue his quests.
Once you've got full Silver/Tungsten gear, build a large, open room on the surface of the Corruption/Crimson biome with lots of platforms, a Campfire, and a Star in a Bottle. This is where you'll be summoning bosses to fight them on your terms.

The first boss (with a Suspicious-Looking Eye) must be summoned at night (after 7:30 PM) and defeated before dawn (4:30 AM)
- The second (with Worm Food/Crimson Spine) can be summoned at any time, but you must be in Corruption or Crimson, respectively.
Many more bosses and better gear can be found further out and further down into the world.
When you get the ability to destroy Corrupt/Crimson altars, keep at least one easily-accessible one intact.