I have HSA.My spouse doesn't.My HDHP covers myself+children from prior marriage. My spouse has own health ins. Do I chk HDHP covered "self" or "family" if filing jointly?

Check "Family". The following is a paraphrase of an answer by SuperUser Opus 17 if you want an explanation. Please feel free to post any additional details or questions in the comment section. 

To be eligible to contribute to an HSA, a person must have HSA-eligible insurance AND have no other medical insurance available to them (except for certain narrow category of exceptions.)  But an HSA, like an IRA, is owned by one specific person.  There is no such thing as a "family" HSA, even though a person may have family insurance.  You are covered by a family HSA-eligible insurance policy, but your spouse also has other medical insurance, so she is not eligible to make contributions to an HSA owned by you.  You are covered by HSA-eligible insurance and has no other medical insurance, so you are eligible to make contributions to an HSA.  Because your policy is a family policy, you are eligible to make up to $6750 in contributions for 2017.

The fact that your spouse has secondary coverage means they can't contribute to an HSA, but it doesn't affect your ability to contribute to an HSA you own as long as you have no other secondary coverage.