Glenna,
LC is very flexible as to size of strips, so it's pretty much a matter of personal preference. In the quilt I have above, the hearth squares are all cut 2.5 inches, for a finished 2 inch square. The individual logs are all between 1 1/4 inches and 2 1/2 inches -- that's right -- I used varying widths of strips. I simply trimmed the blocks to be uniform size before assembling the rows. Some people do like to cut all their log pieces before sewing. I don't. I just assembly line construct the blocks, then press, and cut. It makes the process move quickly for me, and I'm satisfied with my end results.
Since you are new to the pattern, you might find it best to start with a small project (a pillow or a table runner) and use relatively wide strips until you feel comfortable with the construction process.
Have fun with it
RST