I don't recommend Pentium D and Pentium 4 is a little iffy unless you want hassle-free W98 compatibility with AGP. The Legacy of Kain series, except for the last entry is late 90's. Getting a s775 board with AGP and the right chipset for easy W98 can be difficult.

It's better to go on the Core2 route purely for XP. Pentium Dual Cores and Core2 Duos are cheap and they can cover all the XP era. Something like $10-15 almost regardless the model. Sometimes with motherboard. If it's XP only, then look for a motherboard with G3x, P3x, G4x or P4x chipset.

As for CPU, anything is fine from the Pentium Dual Core E5000 to the Core2 Duo E8000 series.

For graphics card, on a budget Radeon X700 (though no SM3.0 support), Geforce 7600GT or Radeon X1650, for more performance but still on a budget GT240, 9600GT, 8800/9800GT, GTS450 GDDR5 GT740, GTX750.

You might also want a cheap Sound Blaster for EAX. Audigy 2 SB0350 or X-fi SB0460.

Edit:

Or you can build THIS for both early XP and late W98. Most of it is cheap and fairly easy to find.

You want run games with full specs or period build? full specs usually require hardware from the next generation Personably I think this is the better option as you don't really notice the hardware when playing but you do notice the games performance, plus it works out cheaper 😀

775 is a good choice for XP. Cheap, plentiful, and fast enough for even the most demanding XP game. It's even period correct!
CPU I've nothing to add to RandomStranges comments above.

For a pure XP build I wouldn't use AGP as it limits your choices as you will want the latest card possible and it'll still hold back the system.
If you get something with PCIe you can go as high as GeForce Titan Z, not that anything in XP needs something so powerful.
Of course if you want AGP for nostalgia reasons that's 100% a valid reason. Get the fastest AGP card that you can find and afford.
Both AGP and earlier PCIe cards are period correct.

I have stupidly overpowered pair of GTX590's in my XP build that plays everything I throw at it at max settings and driver enhancements enabled.
Really you don't need anything like that but would think something a with around the same performance as a GTX570 is enough to have AA,AF etc all at the highest settings and still have headroom for games.

Fully agree you really want an EAX card. Plenty of games used this during XP's lifetime and was totally killed off after XP.
EMU20K2 based cards like the X-Fi Titanium (Not the HD) are the last cards to support XP

I've seen some motherboards out there with support for Core 2 Quad CPUs, but using an Nvidia chipset. They use PCIe for graphics card options, so there's that benefit.

They also have support for IDE and Floppy. Both are a must for me since whatever PC I build needs them. Especially the IDE option since I can use an IDE DVD drive and use cd-audio and cd-digital cables connected to a Sound Blaster Audigy 1 or 2 cards. The floppy is mostly for backward compatibly with older computers in my storage. I have a few Abit Motherboards that require both Win XP and floppy drives to install drivers and bios for.

To be frank, I'll probably run any games off a 4:3 monitor, likely a CRT running at 1024x768 resolution. A lot of those games that I listed don't play nicely with higher resolutions, and I have a few CRTs and LCDs on hand that can run at such resolutions easily.

I would prefer an AGP card, but Core 2 Quad pairs nicely with a Nvidia GTX 750 (or ti model). So I dunno what I'll do, honestly.

As I was setting up SLI I had to go with Nvida chipset. I ended up getting the Asus P5N-D with the 750i chipset which has IDE and Floppy connections.
I remember wasn't much difference between the 650 and 750 SLI chipset's (at least for a XP build) and only reason I got the 750 was someone in China was selling excess new stock boards for about the same price as a used 650 at the time.
Haven't had any issues at all. I'm using a X3320 I pulled from a server with a dead motherboard so not the fastest chip either. I'd like to upgrade to a faster CPU just for the sake of it but truth is the currant one is performing just fine.

I've a Gotek attached to the floppy which is useful for installing XP where I can just have a disk with the RAID /AHCI drivers rather then having to mess around with nlite.
As you say XP is quite useful for creating disks for older PC's as well.
I didn't end up using IDE as XP supports CD Audio over the sata cable. While I have a nice stockpile of both IDE and SATA drives I figure I'll save IDE for 9x and below where the audio cable is more needed.

I only upgraded from 1024x768 to 1600x900 last year when I had to start working from home and the larger screens meant I no longer had space for my CRT or the 5:4 screens 🙁 But I agree a lot of the games are still running at 1024x768

I would say if you have old hardware just try that first. Originally I was using a Asus P5KPL-AM which also had IDE and floppy I had gotten for free. (Actually I got 2) only reason for the upgrade was the SLI requirement.

These topics come up a lot, particularly with XP era stuff, and I always find them difficult to answer. You want something that feels authentic, which is understandable, but is also way better than what you could have got in the past. It is pretty easy to see what the top of the line hardware was in 2000 or 2002 or what have you, but what you are probably going to be the most happy with is what ever hardware "feels" most correct to you. I don't know how to give the best answer to that.

When it comes to AGP cards they are all pretty expensive these days, and the late AGP era cards are often yet more expensive and harder to find. You can save yourself a ton of money and get a PCIE card. A gerforce 6 series or a radeon x800 or x1000 series card is period correct and their PCIE cousins are easily found for 20$ compared to the 100+ dollars you might pay for say a 7950 AGP variant or a 6800 ultra. Personally, I would recommend the GTS 250 or even later. The GTS 250 is a G92b die, which is the last revision based on the 8800 series, and it offers both cool operation and adequate performance to max out anything you like released before about 2006, while still giving you enough performance to stuggle through crysis and get a very decent experience with later XP/Vista era games if you want.

And as for pentium 4 CPUs, if you must get a pentium 4 instead of a core 2duo or later XP friendly CPU/platform, then at least get a cedar mill 65nm p4 on a socket 775 board. The cedar mill was the last revision of the pentium IV and it ran much cooler than the prescott and northwood predecessors. Get a later revision socket 775 board too IMO, like a p45 or p43 chipset, so you can throw in a nice core2duo later if you want too.

Just a general note, the 1999-2001 era of games sometimes have trouble with HT or multi threaded systems. My preferred solution is to get a platform that offers the ability to disable HT and cores in the bios so I can just use a single core CPU when I want, a multi core CPU when I want. That isn't tyically on offer until ivy bridge/sandy bridge. A lot (most) of those games can be patched though, or worked around in other ways.

If you're a serial game player, like to hammer a game to death for a month before moving onto the next, then maybe grabbing a celeron 420, 440 or 460 for a core 2 system would let you switch out for a single core when the need arises. If you like the continually available smorgasbord or buffet of games that has single core sensitive games, then maybe it isn't so suitable.

With the full-range of XP Games, you really want to throw together a vintage system that is as new and powerful as possible, ideally something like you'd see on the shelves around the time Windows XP was replaced with Vista, with PCIe 2.0 for the GPU and multiple PCI slots for soundcards, one being a SoundBlaster and the other a Aureal3D card of good quality. As neato as it might sound to assemble a system of earlier vintage, the older the hardware, the more problems you are likely to encounter and the less powerful the hardware will be. It should have a quad-core CPU, SATA SSDs, and dual-channel matched pair DDR3 RAM. Donor computers like that can occasionally be found at thrift stores or through electronics recycling companies.