The gauge seems to be one that is most easily had using a worsted/aran weight yarn. For examle, you can see in the second pattern you posted that it uses Rowan Summer Tweed. You are aiming for the guage in the patterns, 18 or 19 sts over 4". You might be able to do this with DK weight yarn, but the fabric will probably be kind of loose. Of course, if you are comfortable with adjusting the number of stitches the pattern calls for according to the gauge you are getting, then you can use any yarn. But if not, it’s best to stick with the pattern’s gauge.