The "about 3 days" is key - are you tight for time, or do you have some flexibility? Most of the Similan liveaboards are (at least) 4D/4N trips - and most (all?) leave from the Tab Lamu pier on the west coast, north of the airport, in the evening (7pm? 8pm?). The 2D/2N Hin Daeng trip (Giamani) leaves from Chalong Pier down on the southeastern coast, again, in the early evening. Chalong is where most/all of the day trip boats leave from. Depending on how you're arriving (i.e. what time your flight lands), you may land in time to catch one of the boats out that evening, or you may not. If you don't, then your next day may be "wasted" (diving-wise), if all you're doing is Similan live-aboard, since I don't think you can do a day trip from Chalong and get back up to Tab Lamu in time for the boats. You'd need to check whether there's enough time in between. To get three days of diving in, after landing at around 8pm, I did a day trip (to King Cruiser) and then boarded the 2D/N Giamani that evening, and there wasn't a heck of a lot of time in between my return and when the boat left, so I don't think I'd have the 2+ hours to get from there to the other pier. It's possible there are day trips from Tab Lamu Pier, but I'm not sure where they'd go since I don't think you can do the Similan sites on a day-trip (except by speedboat, and I think that's much more expensive and you only get 2 dives in). (This also assumes you won't be coming in off a crazy flight with serious jet-lag, and so able to get up early the next day and dive.)
So, if you can swing it, I'd recommend getting in to HKT by 4 or 5pm or so, so that you have time to catch a Similan liveaboard. And while there may be some 3-day Similan trips, my guess is that you'll have better luck finding (and more fun on) a 4D/N trip from there. On the boats, there are usually enough experienced divers that you won't be grouped with people too far outside your experience. On my Pawara trip, I think we had about 6 or 7 different groups (for a total of 20 divers), and I don't recall any issues with mis-matched groups. A few folks brought their own instructors, and the rest of us were split between boat provided instructors (who were all great). Though the Giamani is small enough (max 10, I think, with 3 DMs/instructors) that there's slight more of a risk of that with them.
If your time is shorter than that, you can do the Giamani or you may be "stuck" doing day trips from Chalong - though if you're only diving 3 days, you'll certainly be able to do different dives each day. I believe that most of the day trip boats are "cattle cars" run by one operator, but filled by other divers sourced by dive shops. But everyone that's getting certified will be with their own instructor, so you won't be diving with them. The only time I've gone on those boats, it's been through a local dive shop (Andy's) that sends a DM (who are all actually PADI instructors, I think) with you so I've never had to dive with anyone else. What happens to people that book directly through the boat operator (or with a dive shop that doesn't provide a DM/Instructor)? I don't know - I assume they get grouped with other "fun divers" like them and paired with a boat provided DM. Others (stevenl?) can speak more authoritatively on that question.
And, remember, you need to calculate in your post-dive surface requirement before flying, so depending on how conservative you are, you've got another 24 hours on in Phuket after you're done diving (unless you're leaving by land).
So, if you can swing it, I'd recommend getting in to HKT by 4 or 5pm or so, so that you have time to catch a Similan liveaboard. And while there may be some 3-day Similan trips, my guess is that you'll have better luck finding (and more fun on) a 4D/N trip from there. On the boats, there are usually enough experienced divers that you won't be grouped with people too far outside your experience. On my Pawara trip, I think we had about 6 or 7 different groups (for a total of 20 divers), and I don't recall any issues with mis-matched groups. A few folks brought their own instructors, and the rest of us were split between boat provided instructors (who were all great). Though the Giamani is small enough (max 10, I think, with 3 DMs/instructors) that there's slight more of a risk of that with them.
If your time is shorter than that, you can do the Giamani or you may be "stuck" doing day trips from Chalong - though if you're only diving 3 days, you'll certainly be able to do different dives each day. I believe that most of the day trip boats are "cattle cars" run by one operator, but filled by other divers sourced by dive shops. But everyone that's getting certified will be with their own instructor, so you won't be diving with them. The only time I've gone on those boats, it's been through a local dive shop (Andy's) that sends a DM (who are all actually PADI instructors, I think) with you so I've never had to dive with anyone else. What happens to people that book directly through the boat operator (or with a dive shop that doesn't provide a DM/Instructor)? I don't know - I assume they get grouped with other "fun divers" like them and paired with a boat provided DM. Others (stevenl?) can speak more authoritatively on that question.
And, remember, you need to calculate in your post-dive surface requirement before flying, so depending on how conservative you are, you've got another 24 hours on in Phuket after you're done diving (unless you're leaving by land).