The first ones I ever played were Gold/Silver when they were new. Then I backtracked to Red/Blue/Yellow. If you wanted to start "at the beginning" you could try to find the original red and blue versions, but if I was you I would just go ahead and get their GBA remakes, FireRed and LeafGreen. If you ever get any of the DS Pokemon games, you can send your FR/LG team over using the GBA cartridge on the DS.
My other suggestion would be to skip all the games, and go for the newest installment: Platinum. The Pokemon series isn't story driven, so you wouldn't be missing anything. All the games are generally the same, but the newer the installment, the more features and Pokemon it has.