My personal pick would probably the the ones from the 4th gen. For whatever reason, I got much more firmly attached to my first ever captures in Sinnoh than I did in any other region, them including, naturally, starly and bidoof. This might partly be due to Sinnoh's not having a lot of new pokémon that show up early, but not at the very beginning. It was kind of harder for my zigzagoon to get much attention when I took such a liking to the new and exciting sableye and lotad quite early on, while Sinnoh had fewer new, exciting things to get really attached to early on.
It doesn't help that it's pretty seldom that a trainer gets in the position of needing a normal type (and being able to get something completely immune to fighters' attacks from right next door to the fighting gym kind of reduces the necessity of something that might be able to deal super effective damage), so the only potential reason left to keep taillow in Hoenn was for flying on, and I'd caught a swablu that I liked more by the time that became an issue. Zigzagoon also probably registered less easily to me as something to surf on than the actual water type bibarel, so that could have cost zigzagoon its chance for me as a surfer as well.
I probably also like bibarel for being a beaver, because I kind of like them, being Canadian. Bidoof's major unpopularity probably gave it a lot of underdog appeal for me as well. As for staraptor, now that I think of it, I've never really found the regional common birds all that interesting or likeable. While I might say I probably find staraptor my favourite out of a mediocre bunch, my staravia/staraptor did make itself memorable for me with the constant delays it caused with its ability. A lot of the time my staravia was probably the fastest member of my team, so if I got stuck in an encounter I wanted to leave, I'd have to send it out to make my escape, and every time, the thing had to make the ordeal last longer by taking extra time to scare the tail off whatever I was trying to get away from with intimidate. The feathery imp.
My two favorites are the Starly and Bidoof lines, I think 4th gen did everything perfectly when it comes to these two regional traditions.
Other than those, I also like the Taillow, Sentret, Patrat and Zigzagoon lines.
For the rodent it would have to be Sentret 'cause it's so freakin' cute and Furret helped out a bit in my HeartGold game. Bidoof's a close second though since it's also pretty adorable.
The bird would have to be Starly. The black,white, and gray colors look so good on it and like Furret, Staraptor was a useful member of my team in Diamond. It was actually my second most used party member.