What would you like to see in your rival? Your best friend whose friendship you eventually lost, and is always a step ahead of you? (RGBY), A Mysterious Juvenile Delinquent Baddas who opens up as the game progresses? (GSC), just your neighbor who is your friend and pussies out halfway through the game? (RSE), or your best friend who you form a small "rivarly" out of good sportmanship (DPPt), or something brand new?
Personally, I'd like to see a mixture of both Blue and Silver. A guy who's been picking on you for as long as you can remember and picks the starter Pokemon stronger to yours because he wants to beat you (As in, he actually says he'll pick the starter type who beats yours), then he's always causing trouble throughout the region's cities/towns, and ends up as the Pokemon League Champion, and after you dethrone him as the champion, you can meet him and battle him elsewhere once a week and he opens up to you. (As a side note, I'd like the League to actually change after you defeat the Champion. Not every time you beat him, just the first time, with each Elite Four member moving up a rank, so everyone's still there along with a new 1st E4 member.)
Personally, I'd like to see a mixture of both Blue and Silver. A guy who's been picking on you for as long as you can remember and picks the starter Pokemon stronger to yours because he wants to beat you (As in, he actually says he'll pick the starter type who beats yours), then he's always causing trouble throughout the region's cities/towns, and ends up as the Pokemon League Champion, and after you dethrone him as the champion, you can meet him and battle him elsewhere once a week and he opens up to you. (As a side note, I'd like the League to actually change after you defeat the Champion. Not every time you beat him, just the first time, with each Elite Four member moving up a rank, so everyone's still there along with a new 1st E4 member.)