Most gun shops sell inexpensive reloads, usually in a plastic bag or generic boxes. If just for the pistol, these should be fine especially since they'll more than likely be loaded with semi wad cutter bullets. Not good for smooth functioning through some lever action rifles. For dual purpose, stick to specific cowboy ammo. They'll be loaded with round nose flat point bullets.
Neither the wrong way, nor the right, but here's how I started into reloading 20 years ago.
I bought 2 reloading manuals. If I had known about Lyman's manual, it would have been one of them. Instead, I bought a Speer and a Hornady, both of which have worked out fine for me. Leverfan has some good suggestions on manuals.
Against a friend's objections, I bought a Lee Turret with auto indexing in 38 spec. and a Lee powder drop. He wanted me to buy a RCBS Rockchucker. A good single stage press, but on the pricey side at the time. I soon got into IPSC and Bullseye and now wish Dillon was around then. But I had the time and had no problems loading up a couple of hundred rounds per week. Not a whole bunch by any means, but way more than we use for CAS matches. I still use the same press now, but only shoot CAS.
So, you gotta decide just what you're going to be doing. If you think you'll be getting into some of the other disciplines or doing a lot of practice between CAS matches, you'd probably want to save up for a progressive press. The more shooting and reloading you do, the quicker you make up for the start up cost.
If CAS is all you're interested in and your budget only allows for one match per month with moderate practice in between, the Lee would probably work just fine for you and you'd still make up the start up cost fairly quickly, considering how much cowboy ammo costs compared to your own reloads. I used to buy generic reloads for $8 per 50 rounds. I reloaded the same for less than $4.
Btw, TJ has it right. I actually got more from Bullseye since I was loading 2.9 grs. under a 158gr. bullet.