My advice would be to buy a complete bike that "mostly" fits the bill & needs. Part by part builds are way more expensive.
Put it this way:
I bought my tri bike(carbon fiber everything) used for $400 complete. Only changed the seat post purchase.

I bought an old 1974 bike to convert to fixed gear-
Bike: $30
Mustache handlebars:$25
New rear flip flop hub wheel: $80
New tire: $20
Fixed 17T cog: $25
Lockring: $10
Seatpost(bike had no seatpost but did have a seat): $20
New chain: $10

It adds up quickly. I wouldn't trade the learning experience or bike knowledge I gained by building it, plus knowing I can fix it myself is cool. But cost wise and practicality wise, complete is the way to go.