There are so many ways to get into reloading, some are good and some not so good. Since you mentioned you would like to keep the initial costs down I won't suggest a RCBS Rock Chucker Supreme Kit even though it's a great setup. There are a few Lee kits available that will cost you less without giving up too much in quality if anything.
I bought a Lee Classic 4 Hole Turret Press kit about 5.5 years ago and it's served me very will. Even though it's usually a good idea to start reloading on a single stage press the Lee turret press has an auto-index rod which can be easily removed causing the turret press to act like a single stage press. You can go slow at first and when you are more comfortable with the procedure use the auto-index feature.
Kempf Gun Shop online has a great deal on the
Lee Classic 4 Hole Turret Press kit and I highly recommend it. You get to choose the dies you want with the kit so you can get the 4 piece 38/357 Carbide die set with the kit at no additional cost. I also highly suggest buying both upgrades for a total additional cost of only $22. It consists of the Pro Auto-Disk Powder Measure instead of the standard model with is a very good upgrade and the Large and Small Primer system instead of getting only one size. For the price of $199.95 you get most of what you need to start. Add a scale, load manual and components and you're good to go.
After a while you might want to buy some other tools to make things easier but those tools aren't "necessary" for loading quality ammo. Additional turrets for adding calibers to your set are under $10 each. The Lee adjustible charge bar is nice to have too but again, not necessary. (also just under $10) If you're looking for a good tumbler I recently bought a Cabela's 400 tumbler and it's money well spent IMO. It's made by Berry's and considered to be one of the best. The only difference is the color, instead of Berry's Blue it's Cabela's Green... LOL
Good luck and JUST DO IT!!!!