Pietta likely the best option for a single action revolver these days, that won't break the bank. The Pietta 1873 with 4 /34" barrel is compact, fast handling and well balanced in the hand. Very easy to service and maintain. OEM and aftermarket parts are also readily available. The .357/.38 is a versatile choice. Ammo and reloading components are inexpensive and widely available(at least until Covid hit. Supplies are limited, right now).
Edit: To echo Dogzilla's comments: The Uberti Cattleman is also a good choice. If your budget will handle it, the Ruger New Vaquero is an outstanding choice, in a durable, dependable revolver. The Vaquero is built like a tank and easily capable of withstanding the hard use of Cowboy Action competition. For that reason, you will see the Vaquero in the hands of most of the top competitors in the sport. If you plan to eventually compete, the New Vaquero is a sound choice. The Vaquero with 4 5/8" barrel is nicely balanced, points well and fast handling. Next: Ruger Blackhawk. Less expensive than the Vaquero, but just as durable. Replacement parts for Ruger revolvers are also widely available.