For Reborn, I started with Infernape and just wanted to fill the rest of my Team with Pokemon that I liked / was interested in using that didn't share the Fire or Fighting Typing with it. First, I found Budew through the Peridot Ward Event. Then, I trained a Biberal and traded it away for an Abra (Old Version) [Event now gives Litleo]. I caught a few filler Pokemon, such as Raticate, in order to help me stand up to Julia and Florinia. Then, I got Marill from the Jasper Ward Event and Mareep from the Jasper Police Station (Old Version) [Mystery Egg is given by Jasper Police and Mareep is 100% Event in Jasper]. Then, I found a Ground Type in Donphan and my Team was complete!
. . .That was until X and Y came around and two Pokemon interested me. First, Diggersby piqued by interest because of Huge Power and Swords Dance. Also,it would form the "Double Bunny" Core with Azumarill. Malamar also interested me because of Contrary and Topsy Turvy, and later it truly showed its worth because of Topsy Turvy creating the Inverse Field.
My Reborn Team can be found in my Signature.
For Rejuvenation, I wanted the Types of my Pokemon to mirror the Types of my Reborn Pokemon due to Rejuvenation receiving inspiration from Reborn. However, I ended up leaving one Type (Dragon) out of the mix due to Typhlosion being amazing. My Rejuvenation Team can also be found in the signature.
In short, I build my Team simply by using Pokemon that I personally like while making sure that none of their Types overlap. If the Pokemon I use aren't very commonly used, that's a bonus!