I like my 1982 Peugeot PXN 10 which was a racing bike back in the day. I used to own a step down model (a PKN 10) that I trained on regularly with all the local racers. The biggest differences from back in the day when I raced are that I run my handlebars a bit higher than I used to, I run a little fatter tires at a little lower pressure (28c rather than 23/25), and I run a little lower gears (48/36 rather than 52/42 up front and a bigger freewheel, 14-28 rather than 13-23).
So yeah get a racing bike if you want but think about (a) position; (b) tire choices; and (c) gearing (which isn't much of an issue on modern bikes but worth thinking about if you like riding hills--I do).
