Hello and welcome to the forums 😁.

You have a lot of choices! The games you want to play are a great combination of not that demanding and not that picky about hardware. My first advice would be if there is any kind of hardware that you love or have fond memories of, you can definitely build a PC around that and it will work just fine. ​

As for aluminum cases, Lian Li is famous for them. They aren't cheap and their resale value is always pretty high, but you can definitely find them.

If you have any interest in playing DOS games or earlier windows games (like before 2000) then you might consider a windows 98 machine. Early windows games are more particular and the hardware I would recommend for a windows 98 machine is very different from an XP machine.

If you have interest in later XP games then a period correct or over powered XP machine might be better.

My favorite platform for XP is sandy bridge/ivy bridge. Any i3 processor will be an order of magnitude quicker than you need. Sandy bridge motherboards usually support IDE emulation and have at least a couple of PCI cards. They are also very cheap not at all hard to find.

You will want to get an X-FI sound card as well, the X-FI extreme music or gaming are great and cheap. You can get an X-Fi titanium if you want, and they aren't all that expensive, but the extra features aren't all that meaningful.

As for a video card, again so many options! I would say get the fastest nvidia card you can for less than 40$. A GTX 460 is a good card. If you want to stay closer to period correct a GTX 260 is also plenty fast. There are a lots of good options.

GTA SA is my 2nd most demanding XP game (Farming Simulator 2013 been the most) so will give my experience

Socket 775 is perfect IMHO. but wouldn't limit myself to P4. Faster is always better, but you don't need to go crazy just fastest you can get for a good price.
For reference I'm using a x3320 2.50Ghz I got for free and never had a bottleneck caused by CPU.

Graphics I have a HD4890 which does struggle a bit if all driver enhancements are turned on.
Upgrading to GTX590 was total overkill so the GTX460 is probably a good middle ground.

PSU will more or less be decided by the graphics cards requirements, I like modular but that's personal preference.

Case wise as above anything aluminium isn't going to be cheap. That'll come down to price and availability.

Sound I 100% agree with the above . I don't have the best ears but I could definitely tell the difference between the X-FI and the Audigy 2 ZS. Even the OEM X-Fi sounds good although haven't compared as closely.
In saying that the Audigy cards are very good as well if you cant find X-Fi locally.

The thing about early 2000's era is you are getting stuck in the transition from AGP to PCIe. I built an Athlon 64, Geforce 6800 GT build last year, targeting 2004 and the first computer I had some real money in my pocket to buy back then. I had a real sentimental attachment to that specific combo of parts. Unfortunately they left me on the wrong side of the AGP to PCIe transition. The higher end AGP cards I'd need to keep the build in proper working order keep going up and up and up in price, are plagued with reliability issues, especially in the VRAM. A value card from 4 years later with XP drivers is sadly not a viable option. So I'm wishing I'd just gotten over my nostalgia and gone with a PCIe based system. Even latter Socket 939 motherboards would have done the job. Gives you a ton more flexibility in terms of the sorts of graphics cards you can put in there.

If you have your heart set on the P4, believe me, I get it. The heart wants what the heart wants. But from a performance, power consumption and heat perspective, almost everything is better. Athlon 64, Athlon X2, and especially a Core 2 system. Still, that starts pushing into the latter half of the 2000's. That said, from a budget perspective, it feels like there are P4 systems under every rock and around every corner. Old P4 office machines show up every day on the usual resale sights, even local ones.

My Xp system (listed in my signature) cost me under 200 bucks total but of course it's housed in a much cheaper case. It runs games from 1999
to 2006ish ok plus does just fine with Dosbox. Sampling of games: Motorcross Madnesss 2, NCAA Football 99, Return to Castle Wolfenstein,
Serious Sam 1/2, Doom 3, Far Cry 1, Quake 4. Heck I even got some GOG games recently to run on it.

IMO Cooler Master ATCS cases are synonymous with early 2000s high-end gaming PCs.

I’ve got an ATCS 201-SXK, and ATCS 210, an ATCS 111 and an ATCS 620.

this video from phil's copmputer lab was quite good i thought, a 775 p4 system

https://www.youtube.com/watch?v=BRC9Bi3Cj6Y

it's one possible approach

I like my P4's, or did. Which is a change, because I didn't like them at all during their actual era. But, for reasons mentioned by others above, they can also be a pain in some ways. Depending upon the stability of parts you find, and what software you want to run, you might still have a very good experience!

I had fun with them for awhile but ultimately various stability issues, legacy limitations, and inadequacy at the higher end of the era, has caused me to move on to later Athlon (X2) or even C2D stuff, to more reliably cover the 2000-2010 era.