Get the kilo, and gradually replace parts with ones that appeal to you more, or wear out. While you are doing that, you could potentially be getting a better concept of an ideal frame/parts that you "really" want, and eventually get. In my case, I started with a stock fuji track (~'05), swapped out the saddle and bars, rode it for a year or so, and developed a liking for vintage track bikes. I eventually sold the fuji, and now have 2 vintage track bikes (a '76 fuji and a '79 raleigh) built up with mostly vintage parts. The pursuit of the old frames and parts is almost as much fun as riding them. You may find your kilo (or whatever) suits you fine and leave it at that, or you may prefer something else eventually. But getting a basic track bike and working on it yourself is a great way to learn about bikes and develop preferences based on your tastes and less so based on internet consensus of what you should like/get. imo.
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1989 Schwinn Paramount OS
1980 Mclean/Silk Hope Sport Touring
1983 Bianchi pista
1976 Fuji Feather track
1979 raleigh track
"I've consulted my sources and I'm pretty sure your derailleur does not exist"