Should I use bunkers as part of my initial wall-in?
No, this will cause you to spend 100 minerals into a Bunker instead of 100 minerals into the next logical step of your BO, you will miss a Supply Depot and get a Supply Block or you build the Refinery later so you will not have the Gas for a Factory/Addon/Upgrade when you need it.
What can I use bunkers for?
A bunker is a defensive building that has 400 life points, which is roughly equal to the life points of about 9 Marines, so killing a Bunker with 4 Marines actually requires the opponent to kill 13 Marines.
This delays the opponent and allows you to produce less units, gets even better if you repair them.
By creating less production buildings and producing less units you free up Minerals and Gas which can be used to throw down an expansion or research technology.
This can allow you to get Tanks to become more defensive or perhaps a quick Banshee Eco Harass while your bunker(s) hold off those 4 Stalkers (in a 4 Warpgate + Proxy Pylon setting) that planned to go up your ramp so they can warp in 4 Zealots. Too bad for him, you could've even scouted him not producing any units back home so you knew this was coming...
A bunker isn't there to counter a specific threat, it is there to defend your smaller amount of units untill you get your real counter out.
What if my bunker makes them run to my teammates?
And if they run to your teammate, they will either run into his army or a similar defense. You can group up some marines and hellions/tanks and run behind your enemy so he gets attacked from both sides while refilling bunkers, putting tanks in siege mode, expanding or preparing a M/M/Hellion drop.
As said in my other answer, if you also have map vision at this time you can freely do what you want.
Caution: This excludes cloaked units, so get detection at key positions. (minerals, ramp, side, ...)
Should the Terran build bunkers on their own choke behind the wall?
Depends... This allows your units to become more protected as you have a high ground advantage istead of at the bottom of the ramp and you are essentially forcing your opponent to get in a choke point on your ramp. But, if you are planning to expand to a natural that is outside the ramp then you might want to consider to put the bunkers on lower ground instead.