By Infinity Engine I mean Baldur's Gate, Icewind Dale, Planetscape Tormet or Arcanum (there might be others I missed.
Reading about Project Eternity makes me want to try except I never played one and don't know where to start. I've already played the first Fallout and I'm wondering how similar are they to it.

Baldur's Gate 1. Then Baldur's Gate 2. Then Planescape Torment.

Well if you played F1 but not F2 - go for Fallout 2 :-)

Out of those you mentioned - my first pick would be PT and then Arcanum.

The Infinity Engine is realtime, that's the main difference. Arcanum isn't Infinity Engine and if you play it in real time you will end up eating your own face. That being said, ARCANUM. If you want an Inifinity Engine game though, try Baldur's Gate with Trilogy or TuTu installed. If you want your story fix get Torment or if you want more hacky-slashy go for Icewind Dale.

Arcanum is NOT an Infinity Engine game. I would ignore that stupid engine as much as possible. It did to RPGs what Halo did to shooters.

Baldurs Gate 1 is probably the most boring RPG out there. IF you want to play it, play it first, because after playing something decent you won't be able to make it through BG 1.

PS:T is a masterpiece. A must play for every gamer. Arcanum is also an extremely good game. But you only see its real beauty after playing a few of the standard RPGs.

I'd probably go for Baldur's Gate 1 or 2. While 2 is probably the better game, personally the first installment left a bigger impression on me, most likely to do timing. I do think they are both excellent and worth playing though, but as you can see there tends to be a bit of difference of opinion about that. I wouldn't ignore the Icewind Dale series or (especially) Torment by any means, but I think the Baldur's gate series is a good starting point for an introduction to the Infinity games.

Disagree with the people recommending Baldur's Gate; I had fun with it at first, but not enough to recommend it to anyone, and it wore out its welcome before it ended. Completely bland and generic. And it's even worse without Tutu (or Trilogy, I guess; never used that one), and you can't use Tutu unless you also buy BG2, so that's $20 right there. Try Planescape: Torment, is my suggestion.

Baldur's Gate 2 was vastly superior to Baldur's Gate, so if you're one of those people who would NEED TO play the first game before playing the sequel, Planescape: Torment becomes the superior option.

I recommend the Icewind Dale games. I like them all, but Baldur's Gate is my least favorite. If you want something that plays like an adventure game, play Planescape: Torment. There are only a few adventure games I like, so I'm not a big fan of the genre, but Planescape: Torment is still an all-time favorite of mine even if it would have been classified as an adventure game.

As for the Fallout comparison, they're isometric, party-based games. You control the party members though even in the central hero games (Baldur's Gate and P:T), so none of that retard behavior from companions unless you tell them to fearlessly run to their imminent death even if you retreat or they stand in a door way to block you in. You also won't have that silly little bubble around the player character when walls get in the way of view. Also, the inventory is slightly better in Infinity Engine games IMO, unless you're used to playing with mods that make inventory management much better in the Fallout games. All that aside, the talking heads in the Fallout games were fantastic, and the whole setting and atmosphere was brilliant and interesting. The skills and perks were cool too.

As for combat, IE is real time with pause. It can be fine-tuned to pause when certain events happen so it's somewhat close to turn-based if you prefer that. I prefer Temple of Elemental Evil in this regard. Fallout, not so much even though it's turn-based. It's been a while since I played it, but I remember that it pretty much boiled down to get power armor for everyone, get perks that increases both chance and damage dealt by critical hits, shoot enemy in the eyes, and then hope no one suffers a rare critical hit from a super mutant wielding a mini-gun. Fallout Tactics is better if you're looking for combat, but I doubt that's the main draw for anyone wanting to play the Fallout games.

Lastly, Arcanum is not an Infinity Engine game but you still must play it if you liked Fallout.

BG2 for sure. It has a good blend of story and action, so whatever your preferences are with RPGs, it's likely to satisfy them. The story in the first game is quickly explained and is largely irrelevant, so you don't really need to bother with BG1. I played BG2 first and had absolutely no difficulty understanding the plot. Not that BG1 is a bad game exactly, but it was the first IE game and is by far the most primitive. There are some notable spell omissions, too. (Stoneskin, anyone?)

No.

My favourite is Icewind Dale only because it's relatively straightforward and focuses on combat, which I rather like. However, going into it and creating six new characters can be pretty tricky if you're not familiar with the AD&D rules and the general balance of Infinity Engine parties. But the game itself is pretty linear and easy to follow once you clear that hurdle.

Planescape Torment is a stone cold classic, but it is a little weird and the AD&D implementation and class mechanics are pretty wonky for beginners. The writing is amazing, but the combat isn't. You definitely should play it, just maybe not first.

Baldur's Gate is a little generic, but the slow introduction of party members makes it a good introduction to the dynamics and quirks of combat. Ideally I would recommend the Trilogy mod, but if that's a bit too expensive then 2 is better in terms of technology and writing.

Planescape Torment It is by far the great gaming experience you'll ever have... i loved every minute of it :) then Icewind followed by BG. Im a massive Icewind fan though...