I use the default handgun until I get the Punisher. I use that until I get the Red 9. Blacktail is a good option too but Red 9 does more damage.
I prefer the riot gun over the Striker but thats a personal preference. Striker might be better for beginners due to the high ammo capacity.
TMP is just a handgun with more ammo. I almost always use that if I dont want to fire the Red 9.
Broken Butterfly all the way baby! Its free too.
Oh and use your normal shotgun until you get access to the Riot gun or Striker. Dont upgrade the original.