Your starter pokemon become useless immediately when you level up and catch stronger pokemon. Does picking a starter pokemon give you some kind of bonus at some things? Or is it just an irrelevant tutorial thing?
It doesn't really matter which starter you pick, as you can catch all of the starters in the wild, or hatch them from eggs. It is just an ode to how all Pokémon games start, and part of the very brief tutorial thing. You can also just walk away from the 3 starters and get a Pikachu as a starter instead if you wish.
Your starters are very weak in the beginning and you will find stronger pokemon really quickly and be able to evolve them a lot earlier than your starter. Personally I started with a Squirtle but I've found significantly more Bulbasaurs in the wild and ended up evolving an Ivysaur before getting my Squirtle evolution. For a while my starter was actually in my bottom 10 weakest pokemon out of like 40 or so pokemon.
You probably won't even begin to see the starter pokemon regularly until you hit around trainer level 12ish which is important because it means you can't evolve them early.
At the moment, no. Your starter does not matter much. Your starter will be very weak and you will find a replacement very soon after if you hatch eggs. Sadly, your starter will almost certainly be transferred to the meatgrinder and fed to something stronger you find down the line. (Then again, that's entirely your decision!)
But no, your starter is hardly going to be unique or noteworthy in the long-run.
But since terrain and climates can affect what Pokemon you encounter (See Does terrain matter or are the Pokémon's randomly grouped?) it may be slightly more beneficial to pick a starting pokemon that has less probability of being spawned near your area.
All 4 starters are available from 2.0km eggs also.