Depending on the game, Either Type 2 or Type 3. Updated textures are called "HD patch", not "remake".
Type 2 is what I prefer for action oriented games. Changing the genre of a first person shooter (or racing sim, RTS, etc.) seems kinda stupid, for example. So I'd say Type 2 for these genres.
A good Type 3 example would be Final Fantasy VII. I'm totally in for a Type 3 remake here! Why? Because a "normal" FF VII remake won't work at all... Let's be honest:
- The ATB system didn't age very well. You spend 99% of the battles keeping the OK-button pressed to perform normal attacks. Their animations are fast and you don't have to chose anything from the menu. That's something you start pretty early in the game. Normal attacks even become the best damage dealers when you get the 2x-Cut materia (later leveled to 4x-Cut). Yes, I know, there's still Knights of the Round - but that one takes an eternity to cast. And there's the Mime/Limit trick, which is almost so powerful that I'd count it as cheating *lol*. But 4x 9.999 damage with a normal attack? It's the best way to get rid of most mobs! But it's effin boring, too... Updated graphics won't make the battles more interesting. Anything that brings more "action" is a good thing. If I want the original, I play the original (which I do very often).
- The whole feeling of the original game will be gone due to the modern graphics. Just one example: Remember Barret shooting walls all the time when he was angry? That won't work with modern graphics! Back in the 90s it was the best way to show that Barret was seriously pissed. Nowadays he'd look pretty stupid, shooting at random walls while he's talking to the rest of the party. And its not only Barret... Every Character had his/her quirks in the original game. A shitload of tiny details that won't work with modern graphics anymore. All the characters will turn into their Advent Children-versions. You can't prevent that. And then there are all these funny moments, like Hojo wearing his lab coat at the beach... It was funny with the limited possibilities of the original game. It'll look totally out of place in the remake (would work great with Hellsing-like anime graphics). The whole game will feel different because of how different the personalities of the characters will be.
So... Staying close to the original would bring us boring battles (except when you're fighting Emerald and Ruby Weapon) and characters that need to see a shrink ASAP. I don't want that. Better they forget everything that made FF VII great in the 90s and try to do something that'll work today. The original is already available as a Type 1 remake (ported to new OS, added auto saves, tried to fix the sound and the graphics...), we don't need another one like that.
ps. I'm not saying what they're planning for the remake is good. I'm just saying that I think that FF VII needs a Type 3 remake, because everything else won't work.