Howdy
You you have quite a lot of choices.
First off, just let me tell you that there is no Fast Draw in Cowboy Action Shooting. Fast draw competitors shoot blanks, CAS shooters shoot live ammunition. And revolvers that are used in Fast Draw competition are usually heavily modified to put up with the abuse Fast Draw subjects a revolver to.
So, your first choice is Ruger or Colt replica. You are not going to get a real Colt with your budget.
Rugers have a well deserved reputation for toughness and reliability. The mechanism in a Ruger is completely different than the mechanism in a Colt or colt replica. In addition, Rugers use coil springs, which are almost indestructible. With a Ruger you get a transfer bar built into the action, which makes the gun safe to carry fully loaded with six rounds. Rugers look similar on the outside to a Colt but as I said, they are completely different on the inside.
If you want a Ruger that looks mostly like a Colt, you go for the Vaquero, or more properly the New Vaquero. The Vaquero series of revolvers have fixed sights, just like a Colt Single Action Army.
The revolver at the top of this photo is an 'original model' Vaquero. These were larger than a Colt or colt replica, built on the same size frame as Blackhawk. The 'original model' Vaquero was available chambered for 44 Magnum as well as 45 Colt, 44-40, and 357 Magnum and a few other calibers. Ruger produced the 'original model' Vaquero from 1993 until 2005. It is no longer in production.
The bottom revolver in this photo is a New Vaquero. Ruger began producing the New Vaquero in 2005 and it is still in production. The New Vaquero is roughly 10% smaller than the 'original model' Vaquero, bringing it down to the same size as a Colt. The New Vaquero is only available chambered for 357 Magnum and 45 Colt. No 44 Magnum. The cylinder is not large enough to take the pressure of a 44 Magnum. Some special editions of the New Vaquero are available chambered for 44 Special, but not 44 Magnum
Your other main choice for a single action revolver from Ruger is the Blackhawk. This one is chambered for 45 Colt with an auxilliary cylinder for 45 ACP. The Blackhawk is built on the same size frame as the 'original model' Vaquero, so it is available chambered for 45 Colt, 41 Magnum, 357 Magnum and a few other calibers. If you want a 44 Magnum you will have to go for a Super Blackhawk. There are a few other specialty single actions in the Blackhawk line too.
Moving over to the Italian imports, the chief makers are Uberti and Pietta. Pietta used to be an also ran to Uberti, but in recent years their quality has improved.
This is an Uberti Cattleman chambered for 45 Colt. Ubertis and Piettas have a similar mechanism to a Colt. This means there is no transfer bar, so it is strongly advised never to carry them fully loaded with six rounds. If the gun should happen to fall and land on its hammer, it will most likely fire. Import restrictions require Uberti and Pietta to provide a safety device to prevent this, but many shooters remove them to make the gun more convenient and less awkward to shoot. There is one colt replica made by Beretta (the owner of Uberti) that has a transfer bar in it, but most do not.
Ubertis are the same size as a Colt and the mechanism is the same as that in a Colt. That does not mean the parts are interchangeable, they often are not. But they function the same. You have to put the hammer at half cock to free the cylinder to rotate for loading and unloading.
The top revolver in this photo is a 2nd Gen Colt Single Action Army, the lower gun is the Uberti Cattleman.
Uberti makes a pretty good revolver, despite a few shortcuts, but one thing I do not like about Ubertis is they duplicate the old difficult to see 'V' groove rear sight of the 1st Generation Colts. Colt went to a much easier to see square groove a long time ago.
Lastly, a word about reliability. Because the mechanism in an Uberti is basically copied from the Colt, which was modified in 1873 from the earlier Cap & Ball mechanisms, you are dealing with an outmoded design still produced for the sake of nostalgia. The interior parts of these guns are more delicate than the parts in a Ruger. I am not saying that they are going to break the first time you shoot them, but broken bolt/trigger springs do happen. They have happened to me several times. But at least Uberti seems to have replaced their relatively fragile leaf style hand spring with a coil spring these days.
It has left an insatiable urge to own something as close as possible to the real thing.