How many birds you can keep depends on how you are intending to race.
For example, are we talking about JUST a racing loft or an entire loft system?
Most successful racing fanciers would NEVER dream of racing their breeders and their racing team is kept separate from their breeders.
As I mentioned on your other thread asking about keeping two breeds, you really need at minimum a loft with three sections. Two for the breeders and one for the birds you intend to race (MINIMUM).
Most racing fanciers keep at least two lofts: a two section breeding loft and a two or three section racing loft. The name of the game is building up your race team.
If you are limited to just a 6 X 8 X 6 foot loft area, you will find that racing pigeons might be beyond your space limitations unless you do it on a very small scale (only 2 or 3 pairs of breeders and a very small race team). Even though there are advantages to keeping only a few birds, it would be pretty tough to be very competative on this small a scale.
Since you are just starting out and you are young, I would REALLY, REALLY recommend that you find an older racing fancier in your immediate area who will take you under his wing. And if you are VERY LUCKY, that older gentleman will be a top racing guy. Finding the right mentor will put you ahead of your competition, both in birds and guidance, and he will teach you everything you need to succeed at this. Most of those old timers will welcome forging a friendship with a young guy who is willing to carry their work on when they are gone.