I've become interested in creating a few shirts (much like these or this) to put up for download, only thing is I have no idea how to do anything like that! So what are the basics? Point me in the direction of some reliable tutorials and the programs I might need, and tips and advice is always appreciated!

Sounds like you want to add a stencil--this is a good place to start.
http://simswiki.info/Sims_3:Creatin...othing_Stencils

Really good tutorial, walked me through it step by step, but what do I do with the DDS with the stencil now? Like is there a certain location it needs to go? And then how would I go about making a .package with the shirts included? I apologize if these questions sound dumb, I've never worked in this area before.

At the very bottom of the tutorial, there is a link that says "See Adding Custom Stencils to an item" to add your stencil to a CAS part--you'll need to click that link

Awesome! Okay, so I went through it all and successfully created a shirt design, but it is not recolorable in game, is that what should be happening, and if so how would I go about changing the color of the shirt from the default grey?

Wait, I think I know what I did wrong. I didn't take the base layer with the shirt template out before flattening and making it into a DDS file, which made the template part of the stencil.