Ignoring the stats question for a moment...

Your indexes are redundant and unnecessary. You've got a clustered index on a column, then two nonclustered indexes on the same column. The nonclustered indexes aren't necessary at all there.

As for the stats...

The query you posted will likely result in stats being created on the job_status and job_name columns, because there is no index on either column, Ok, without an index there's no way other than a scan to process that query, but still...

Stats is a tough question because there's no easy way to manage them selectively and efficiently, hence many people will just update all stats when they do maintenance. If the maint window is large enough, that works. It's when the DB is too large and the maint window too small that it becomes difficult and, unlike indexes, there's no good guidelines as to when the stats should be updated because it's too dependant on data distribution and queries. Hence if you have time to just update them all, just update them all.