Just beat the campaign and already played beta for a few months so I know a lot about the multiplayer but i'll concentrate my short review on campaign since it seems to what you guys are interested in.
The story is much improved from WoL. Much more captivating and intriguing. However this is more of a knock on the very cliche and predictable story that became of WoL. HOTS story is decent but nothing to write home about. The cinematics were great and the cut scenes were overall done well.
The number of missions was cut down to 20 while WoL had 29. Including the time spent evolving your units and having convos with other characters, this will give you a playtime of anywhere from 9-13 hours. HOTS missions have more of an RPG feel to it with some missions baring striking resemblance to diablo 3. If you have played WoL before, you'll know what to except, varied missions with objectives that go beyond simply building a base and destroying your enemy's base. The missions are again fun but other than 1 mission, they do not cross any boundaries established by WoL.
Final verdict: If you liked WoL's campaign, play this game. If you didn't, this expansion will hardly change your mind about the series. I personally really enjoyed HOTS. The missions were fun and the story was a lot better but I expected more deviation from WoL. It ultimately is more of the same. If you've never played WoL, play it because its one of the best RTS games ever and then decide on HOTS.
This expansion was 3 years in the making but those 3 years were spent on multiplayer, not the single player campaign so don't get your hopes up. With that said, B.net is much improved and Blizzard sent a considerable amount of time trying to bridge the gap between campaign players and multiplayer players. They added a lot of new training modes, more advanced AI for you to face and an unranked laddering system where you can practice your skills against equally skilled opponents without being graded on it.
Note: If your good at SC2 and want a challenge from campaign, skip brutal mode. Play it on hard and try to do the mastery achievements.