This is likely going to be a semi-long list, but here's a few computers I've wanted to build/buy for a while:
A full-tower ATX dual Pentium Pro 200MHz server with 256MB of SDRAM and a few 4 or 8GB SCSI drives in RAID, with a tape backup drive, running Windows NT 4.0 server. This would be a main server to drive a vintage network of "meh," size, running dedicated servers for various late 90's games and running as a file server.
If you're talking going fully unrealistic, I'd really like to have a full-blown internal 56k dial-up network using Pentium III Xeon rack servers and enterprise class network switches and modems and the such, with my own mediocre websites for file directories and other things, and then a few servers dedicated to running a large amount of websites ripped from archive.org and stripped of anything but the original code and files, serving computers in a massive warehouse divided into smaller rooms by year of manufacture for each computer. What I would do with this, I have no idea. I could run a massive multiplayer death match in Quake III or something from the sections 1998 and up? How many people are really going to want to sit in a large, noisy room that sounds like it has 100's of small jets revving in it while playing 20+ year old games? How am I meant to keep said thousands of total computers in optimal shape and dust-free?
I'd like an 8088 based machine at some point, doesn't have to be an IBM, with a 20MB HDD or something like that in it, just to sit down at and mess with DOS and MS Works or some weird stuff like that.
More realistically, I'd like several Pentium II or Pentium III based machines with discrete graphics of some sort in their own little setups to have LAN parties for old games with. I did this before, but on a very limited scale, and there were only two late 90's computers in there, the rest were mid-Windows XP era. There is something far better about playing old games like that with friends in the same room on your own little network than just playing games with people online.