This is a fun hypothetical!
Hypothetically, I live down the road and have known your family for a bit. I would build you something with all spare parts and I'm sure I would've used the $100-ish on parts to make the best thing I could. (this is how I did it, too. I never made any money building PCs back then... or at all, really, 🤣)
I'd build with whatever case I could snag up or just loitering in the scrap pile. Most likely a bit yellow already. Possibly an exoskeleton. The timeless combo of ECS K7S5A and Athlon of some kind. Hopefully a XP. CPU might be a purchase. 1GB of DDR (any pair) so speed might not be great, but the internet is going to work a hell of a lot better. I would've had GF2 and some crappy ATIs laying around at the time. If we're trying to do some gaming together, I'd toss in the GF2. If it just needs to be an office PC, I'd toss anything AGP in. And with that, I'd be using the on-board audio and a 40GB Maxtor. If I didn't have a drive that large, I might be buying a new one, too.
Oh and you KNOW this bad boy would have windows XP on it with the authentic* install media in the bottom of the case. I used to do that a lot. XP would slow the F down after a while of being in the presence of internet, so reinstalls were frequent.
What I was running in 2006 was a MSI 478 board (mATX, can't remember else about it, only that it was red) and a CeleronD 2.8GHZ with 2x512 DDR400, which was BLAZIN' compared to the PIII 550 I upgraded from. I got it at a computer convention and paid less than $200 for it (fall 2005). First computer I ever bought. The Athlon computers we had were hot and slow, so we preferred the Intel ones. Off-loading the AMD stuff is just a good idea.
P.S.: This would be a 12-13 year old kid building your computer.
*Heh, "authentic"
Main Loadout (daily drivers):
Intel TE430VX, Pentium Sy022 (133), Cirrus Logic 5440, SB16 CT1740
ECS K7S5A, A-XP1600+, MSI R9550
ASUS M2N-E, A64X2-4600+, PNY GTX670, SB X-Fi Elite Pro
MSI Z690, Intel 12900K, MSI RTX3090, SB AE-7