Hi. I just got into it about 3 months ago myself. Like you, I had a bunch of brass and figured it was time to start reloading. First off, it is FUN! Whether or not I'm saving money (I am, but I'm also shooting a lot more as well), it is a great hobby.
Secondly, you'll need a kit. I bought the Lee Anniversary Kit from bosesguns.com for around $75, which is about as cheaply as you'll be able to reload for. I am very happy with the kit so far, and have reloaded about 600 rounds with it. It is easy to do, especially if you have a friend who can show you the ropes for the first 100 rounds or so.
In addition to the kit, you'll need bullet dies specific to the caliber you plan to reload - in your case, the .357 magnum (which is the .38 caliber dies). Bosesguns.com sells the 3 piece (you need all 3) Lee carbide dies for only about $19, which, again, is about as cheap as they can be found. The carbide dies are preferrable over regular dies because you don't have to lubricate each round. You'll also need powder, bullets and primers.
Lastly, and importantly, you'll need a couple of reloading manuals. I bought the Lee manual and Speer Manual 13th edition. These manuals tell you how to reload and also give you the recommendations for how much powder of various brands is safe for the caliber and bullet weight you'll be using.
A brass tumbler is nice as well. It makes spent brass all shiney and new looking.
For all of the above, you're looking at around $230. There are more expensive kits out there....RCBS is one that comes to mind. It doesn't incluse anything that the Lee kit is missing. Some people say it's tougher, but Lee has been making this stuff for decades and decades and people swear by Lee as well. Check out the Handloading room on this website.....you'll find TONS of info on reloading.
Hope this helps - it's a very relaxing and fulfilling hobby!