You may not need the children's patch depending on which version you have.
And KillAp's patch includes the official patch (If you want to install both, do official -> KillAp). Ignore the trolls that say not to install KillAP. They don't have any idea what they are talking about.
I...don't have any idea what the "FO2GUP" thing is.
I would recommend only the official patch of FO2, not Killap's unofficial patch. I'm not a troll for firmly believing that one should always play great CRPGs in their vanilla state. It is in fact trolling to say that I'm a troll simply because I'm against unofficial patches, fixpacks and mods.
XD @ the fat kid's rant about bullies. You sound like an after-school program on legs. Big, meaty sausage legs. - Absurd Questions to Thunderlips_, 2008.
With Killapo's unofficial patch, you won't need the children patch or the official 1.02 as the Unofficial one contains both already. At least, I know for a fact it contains the official 1.02. And I know the restoration includes the children. I'm fairly confident the patch includes the children too, but you'll need to check.
And as others have said, you'd only need the children patch anyways if your version is non-US.
I'm Commander Shepard, and this is my favorite board on GameFAQs.
I have the White Box Fallout Trilogy, which I assume is non-US, seeing as the rating is PEGI instead of ESRB.
So I went ahead and installed the Children's Patch, then Killap's, then FO2GUP-Alpha01 (Fallout 2 Graphics Update Patch), and finally the High-Resolution patch. I haven't had any problems yet, the only thing I didn't notice was FO2GUP, but it doesn't really matter to me.
The Hi-Res patch works very well, I haven't had any issues with the graphics like I normally do when playing. (Cutscenes being distorted and pixelated with weird colors like red, white, and blue, or sometimes the screen blacks/whites out and I have to "shave-off" the black/white screen by moving my cursor everywhere on the screen.)