Most performant design for each member to manage his/her own news list?
You need four tables:  

User            Category           Article                  Pivot
+----+-----     +----+-------+     +----+--------+-----     +---------+--------+
| id | ...      | id | title |     | id | cat_id | ...      | user_id | cat_id |
+----+-----     +----+-------+     +----+--------+-----     +---------+--------+


Table Pivot is standing for M:N relation and contains the subscription pairs user:category. Each user can have 0..n categories subscribed and each category can be subscribed by 0..m users. To fetch articles accordingly to the user's subscriptions you need to use JOINs like that:

SELECT u.name  AS UserName
     , c.title AS Category
     , a.id    AS ArticleID
     , a.title AS ArticleTitle
     , a.date  AS ArticleDate
     , a.url   AS ArticleLink
     -- everything you need 
  FROM user      AS u
  JOIN pivot     AS p  ON p.user_id = u.id     -- pivot to user first
  JOIN articles  AS a  ON a.cat_id = p.cat_id  -- articles and
  JOIN category  AS c  ON c.id = p.cat_id      -- categories to pivot then
 WHERE u.id = 12345
 ORDER BY a.date DESC
 LIMIT 10
;


For the best performance you need to index tables by the columns used by the query:
user should have the primary Key (id)
article should have the multicolumn key (id, cat_id, date)
pivot should have the multicolumn primary key (user_id, cat_id) with FKeys to the corresponding tables.