The "DB Error: no such field" bit in your error message is your key clue.
The missing field is listed as "Unknown column 'j.start_date' in 'where clause'", but it's not showing any more of the sql to know which table that comes from.
I dug through some code, and I'm pretty sure it's supposed to be coming from the civicrm_mailing_job.
So - either that ...
You can use find contact search or Advance search or find membership search. Perform search and then select the contact you want to export and from task drop down select export, and select 'Export PRIMARY fields' or 'Select fields for export' if you don't want all fields.
Lots of digging here:
The culprit is Bluehost shared hosting AND VERP (variable envelope return processing), which is an interesting hack and very useful for massive systems. (I am a colleague of Ray Tomlinson and something of a dinosaur when it comes to email protocols ...)
Bluehost is my shared hosting provider (no VERP) and VERP is - well, a hack. VERP ...