I would just be careful you know what you are getting yourself into.
At the end of the day any older bike from that era will be heavier than modern carbon fiber and possibly aluminum bike, probably have less range on gears/bigger jumps in gearing, have less aero, and may not accept modern road wheels. I am a big proponent of a rider focusing on fitness before buying speed, but you also have to be realistic that bike specs help.
Also, potentially doing your own build could end up costing almost as much as a modern Aluminum bike that has entry level modern components (e.g. STI shifters), but not be equivalent in specs once said and done.
For example a pair of STI shifters is probably around $150 for 105, cranks are probably around $250, derailleurs $120, brakes $150, cassette $90, chain $50, seat $90+, grip tape $30, handlebars $100, and then add on miscellaneous costs for any customization or fabrication if needed. This does not include the original cost of the bike frame.
Once you look at it closely a $1200 aluminum bike does not seem all that bad for something that has modern components and a more aero profile.
With that said, if you are doing this knowing you may spend almost as much for a modern bike, but end up with a bike that is not equivalent in performance that is fine, but it seems like you want to do this and end up with a "rat rod" that is on par with a modern road bike of today. I do not think that will be possible otherwise you would see the pros on aluminum bikes from the 90s.
Not knowing your budget, I would seriously look at endurance fit road bikes. I would recommend going to a bike store that has a bike fitter (e.g. Trek Concept Store) as it is pretty common for people to buy a used road bike and have it be the wrong size. I would also consider if you have the funds to buy an entry level full carbon road bike (e.g. Trek Domane SL 5) or try to find one that fits you used as that in my opinion is good balance of cost and longevity (i.e. aluminum tends to crack at the welds sooner than carbon fiber will fail). Also, one watch out with buying a modern road bike used is the frame warranty usually is not transferable to the second owner.