The first Bloodshot series is hit and miss. I would recommend skip it unless you have a burning desire to read more on the character. It ties into Harbinger Wars, but it doesn't contribute much worthwhile as it takes place before the event. Bloodshot Reborn is on another level though, but you don't need to read the first series to get on board with that; just The Valiant.
Make sure to sequence the Harbinger and Harbinger Wars issues (I think there's a guide on the back of the HW trade). Fair warning about Harbinger, the art is rough and inconsistent in certain places in the second volume, but it levels afterwards.
Archer & Armstrong's first series is some high-tier comics. It only ties into Bloodshot much later into the run, and I think the 4th or 5th trade includes those issues for you, so you don't even have to worry about that.
You can skip Shadowman, too.