All bikes, no matter of price, can be slow or fast depending on the rider. Your question should have been, what is the best bike for under $1,000; followed by the kind of riding you want to do.
If you want to do long miles and be comfortable I would look at the Masi Speciale Randonneur SE, even if you like to go fast you will eventually want to go far so comfort may become an issue. This bike is also suited for the road, gravel and light to medium touring, it's a do all type of bike that doesn't excel in any one area of cycling preference, but does them all well.
Another bike like the Masi to consider would be the Salsa Journeyman with Claris components, the components are a bit down graded from the Masi but those can be upgraded when stuff breaks; this bike is made for medium to heavy touring, which means it will do well for long distances, and it will do well on gravel; it leans more toward doing touring and gravel a bit better than the Masi.
But if you don't care about distance and you just want a bike that is capable of going faster than I would look at the Giant Contend AR3, but the geometry of that bike won't be as comfortable on long rides, won't be suited for gravel or light touring.
If you want an even cheaper bike, like around $500, then look at the Schwinn Fastback, this a only a road bike, it won't do well on gravel or touring.
When I say a bike won't do well with touring, that doesn't mean you can't, but if you did you would have to make some changes to the bike, but it would never be good at touring just ok, you could always credit card tour on those types of bikes, and get special quick releases that you can attach a pannier to, but it would have be a light load type of touring.
