The P-Sec Pistol normally isn't a weapon of choice while playing through Dead Space: Extraction, but it's not bad. Also, since you are first introduced to this weapon in this Chapter when playing through the game for the first time, ammunition for it is plentiful in this level.
You don't have long to get the Text Log, Plasma Cutter and ammunition in the starting room, but you still have enough time to collect it all if you are fast. In case you miss something important (like the Plasma Cutter or, more likely, the Text Log), you get another chance at grabbing items when you return to this room later.
After eliminating the doctor who took two hostages (and dealing with the hostages afterward), you'll enter a hallway. While playing, you should clearly notice the first P-Sec Pistol Weapon Upgrade in this hallway. (8:40)
This video ends right after two bodies fall into the hallway (that contains the P-Sec Pistol Weapon Upgrade) before the room before the Plaza.
This video begins right after two bodies fall into the hallway (that contains the P-Sec Pistol Weapon Upgrade) before the room before the Plaza.
I, unintentionally and unfortunately, got hit quite a few times in the Plaza, but I survived and got five stars in the end just fine. The Impossible difficulty mode in Dead Space: Extraction is far more forgiving (damage-wise, anyways) than the same mode in the first Dead Space console game.
Though his comments don't appear in the subtitles, you can actually make out part of what Karklins is mumbling in the Plaza when he and Gabe Weller arrive.
Right after entering P-Sec Headquarters from the Plaza, you can see the second Rivet Gun Weapon Upgrade past Weller's shoulder. (4:07) You can also attempt to get it after you board up the door or when you return to this area later on.
Don't dawdle with boarding up the door. If you take too long, the crazed colonists will burst through and kill you.
In case you missed some items at the beginning of the Chapter, you have another chance to get them above or from the lockers. (6:25)
This video ends just after finding and adding Lexine Murdoch to your group.
This video begins just after finding and adding Lexine Murdoch to your group.
If you didn't get the second Rivet Gun Weapon Upgrade previously, you get another chance after passing the Armory in P-Sec Headquarters. (1:11)
When you head for the shuttle wreckage, you should be able to clearly see the second Plasma Cutter Weapon Upgrade. (6:03)
When you're at the final puzzle of the Chapter, don't bother fighting off the Necromorphs as they'll just constantly respawn. You're far better off just using Stasis on one or two of them to give you enough time to finish the hacking puzzle and move on.