I cut my strips on the lengthwise grain. I THINK I learned that from a Marti Mitchell book.
Even with starting with the selvage as my first guide line, I find it necessary to retrue the strips every so often.
Also, the folding of the fabric is very important. I ignore the cut ends - they end where they end - but I try to have the main folds parallel to each other.
And the I try to have the ruler lined up with the folds.
This also is probably clear as mud.
I've found that sometimes when fabric is processed the grain lines are distorted. I wash and dry them, and then see what I have. If it is extremely off-grain, I won't use it.
I hate the zig-zag cuts.