What I think people are telling you is "Don't stay in Phuket and do day trips".
Ditto what Bowmouth said. There are quite a number of 6 day cruises, those are great. (I did three back to back . . . and like somebody said, never got tired of it).
For choosing a boat, a good bet is to find a booking agency, they have lists of boats and schedules, then you can ask them a million questions and they'll tell you which boat is right for you considering your criteria. I use John Williams at Siam Dive & Sail, but there are others.
Dive areas:
Right around Phuket the diving is so-so, depending on what you're used to. To the south are pinnacles Hin Daeng and Hin Muang, which can be spectacular. We had one day of so-so diving there, and then when I was back a week later, we had a solid day of closeup nonstop incredible manta encounters. This was in late November.
Phi Phi island also has decent diving, but not super spectacular.
The Similans are a chain a few hours north of Phuket. Actually, as you go out there, you first get to Koh Bon usually for one dive (known for Mantas, but not in November IIRC), then one dive at Koh Tachai (my favorite spot, a pinnacle with lots of fish life and can be strong currents), then you motor on out to the Similans for a few days, where there's alot of bathtub diving with prefect blue water, white sand, pretty fishies, pretty coral. Lots of life. Then, if you're on a GOOD trip, the highlight is to head out to Richilieu Rock, another pinnacle a bit past the Similans. Everybody pretty much agrees RR is world class. Tons of fish, cuttlefish, corals, sometimes whalesharks (people saw one my last cruise, late november), absolutely stunning site. Lovely.
So if you do a liveaboard there, make sure it's going to Richilieu.
Further north than that are the Surin islands. Some trips go there. Our couple of dives there were nice, but not that spectacular.
Further north than that is the Mergui Archipelego, in Burma, which is a whole nother thing, becuase there are only a few boats up there - when I went anyway it was very peaceful and serene (some of the dive sites in the Similans can get a little crowded). Lots and lots of fish. We had a whaleshark under the boat that I snorkeled with in my pajamas (couldn't be bothered to undress before leaping in - that was in January). Water in Burma is greener and more nutrient rich, when I was there the schools of fish were much larger. About the same number of large pelagics - i.e., not many - a few mantas here and there, very few sharks, except for fairly reliable sightings of nurse sharks under ledges at around 100'.
If you only have a week, I'd do a 6 day to the similans. If you have 8 or 9 days, I'd do a 6 day to similans plus a 3 day to Hin Daeng/ Hin Muang. If you have more time, I'd do Similans plus Burma. Similans and Burma are very different, however, so I wouldn't skip Similans to do Burma.
There's a bunch of posts on here about the different dive areas and boats. But like the person above said, you need to think of the following:
1. a/c versus no a/c (prolly not needed in late november)
2. private head v. shared.
3. Nitrox v. no.
4. "cushy" boat v. basic.
5. How many divers per boat - some really pack them in, some don't.
6. What areas you want to visit and for how long.
7. What nationality divers does the boat cater to.
8. How much you're willing to spend.
Answer those questions and the booking agent can point you toward the right boat for you.
Good luck and have fun!
