There are two Logs and two Artifacts on chapter 1. Be sure to click on the images for larger versions. Unfortunately, because of the dimness of the game, it's hard to make things out in pictures at less than full screen.
Log 1: Audio
The first log is found in Isaac's apartment (in which you start). Immediately turn right and you'll see a computer lit up. Activate it and you'll hear the audio log.
Log 2: Text
This second log is found in the same room. From the computer, move around the bed to the far side and you'll find this text log sitting on the bed.
Artifact 1: EarthGov
During the course of your gameplay, you'll be blasted into a sewer and then fight through a group of enemies until you come to a road with a bunch of automated cars moving across. You have to freeze these cars with your Stasis ability to progress but after you do, don't go up the ladder. Instead, go into the street and turn left. You'll find a small room (which you could have looked into but not accessed before) and on the floor will be this artifact.
Artifact 2: Unitologist
This Artifact comes after a cutscene where the grand plan is explained to you. After Isaac narrowly escapes death, you'll fight your first Necromorphs on this level. Kill the first two in this room and then the bunch in the next large room. You'll then take an elevator down. Immediately after stepping off, turn right to see a reception area blocked off mostly by a desk. The artifact is right behind this desk.
