I've just gotten Fallout 3 GOTY but I'm new to the Fallout series, never having played 1 or 2. I've been browsing the forum for general advice but most of the posts assume familiarity with the Fallout "world". Can I come straight in with Fallout 3, or should I get 1 & 2 first and work my way through them?
Otherwise, is there some general advice about how to get started? I've played about with a couple of characters so far and I'm enjoying it. My previous RPG experience is mainly with Morrowind, which has taken up many hours of my life!

I started with fo3 as well. If you have a lot of rpg experience you should be good to go. You know just read what the stats do for you and go from there.

I noticed a guy in shiney armour on the cover with a weapon I could not identify, and I figured I was going to be doing some shooting.

This. Pretty much exactly, except the part about BoS on the cover. I like to research as much as I can about a game without spoiling it before buying/playing it. That, and my friend had it way before me so I got pretty good at it.

No, Fallout 3 is a complete "Fallout", you need no knowledge of the early Fallouts 1 and 2. The early Fallouts were turn-based combat play anyway, nothing like the full role-play real-time of Fallout 3, and 3 is complete in storyline and quest-lines. Fallout is a sequel of Fallouts 1 and 2 in the sense that the scenario and the type of content and game-play is of the same nature as those early Fallouts, of quite mature content sometimes.

Once you leave the vault you will be in the Fallout wasteland for real, fairly weak at first but you soon get stronger after some kills and level-ups. Well you've done Morrowind, you know how RPGs go. ... Er no, don't get the early Fallouts and work through them, you will gain nothing useful for playing Fallout 3, I did happen to play the early Fallouts way back when they were out. You are good-to-go.

My tips:

• Science and lockpick are important for all characters
  
• Collect every bit of rubbish early on and sell it.
  
• Don't follow the main quest too closely, there's plenty to do and it can wait.
  
• Speak to everyone and take notice.
  
• Really explore Megaton and it's immediate surroundings.
  
• Load up all the GOTY extras right away but don't play them for a while.
  
• Get the Ghoul mask as soon as possible.
  
• Save frequently (and as you leave the vault)
  
• Oh and there's a lot of useful stuff to be picked up in the vault before you leave.

It's a stand-alone game and can be played as such, no prior experience with the earlier games is necessary either from a story or gameplay perspective. The originals, which are very different to Fo3, are well worth playing in their own right, though. If you've gotten your head around Morrowind, you'll be fine with Fo3, it's pretty accessible and straightforward.

The game is extremely easy after you get a few levels under your belt. My advice: First, dump everything in Small Guns till it's like 75. You can finish it out to 100 with books and the Small Guns bobblehead. Then, if you're having an easy time, put points in Lockpick, Speech, or Science, or if you're dying a lot, put points in Medicine.

My advice would be to put these points into Science, Lockpick and Sneak. Small Guns can wait, really.

But of course, it depends on your personal style. It drives me mad when I am not allowed to use a terminal or a locked door/container because my respective skills are just a tad too low. So this is why I increase them rapidly straight away.

Yes, encounters with Mirelurks or so are a pain under these circumstances, but this is why I put points into Sneak. For the sneak critical damages.

These are pretty good tips, the ones I would add are:

BEST TIP
Get 9 Intelligence when doing Special, then, go to Rivet City right out of the vault and go the Science Lab and get the Intelligence bobblehead. At level four, get the Educated Perk. This will give you a ton of skill point and you will have 100 in all the essentials by the time you get to higher levels. Trust me, this will make a huge difference.

-Try to only specialize in one type of gun set at first. (Big Guns, Small Guns, Energy Weapons, Melee) I would not recommend unarmed. The key is to not try to be the Jack of all trades, it's not Oblivion. You can't do everything, so pick a style and stick with it. It's a lot more effective to be great at one thing than okay at everything,
-Grab the medicine bobblehead in your father's office before taking the G.O.A.T.
-Putting points in Barter and Speech gain save you a loooooot of money.
-If you pick Energy Weapons, do Mothership Zeta first, if you pick small guns, do Point Lookout, if Melee, do the Pitt
-Once you play The Pitt, do the Steel Ingots quest, you will get some great armor and one of the best guns in the game, especially for stealth
-As far as Perks, get Strong Back and Scrounger. They will help a lot.
-Go to Springdale once you leave the vault and find the only shack you can go into, and kill the girl for a quick 400 caps.

Mines are a very good way of dealing with animals such as radscorpions and mirelurks. Just run away in a straight line and drop mines as you go. Once they lock on to you they will follow, and walk right on top of the mines. Another handy mine trick is to sneak up on someone, set up some mines between you and them, then back up and start shooting. If they charge you, boom! Setting up bottlecap mines like this is a great way to deal with deathclaws.