The different types of Langstroth Bee Hives depend on your climate and physical ability.
I am still a novice beekeeper. But in my few years of beekeeping I have accumulated 7 beehives, all variations on the Langstroth classic design. The Langstroth design is the beehive that has removable frames for harvesting from the top of the hive. Therefore you do not have to destroy any honeycomb when harvesting honey and you can return the frames with comb right after harvesting.
When I first started taking bee classes, the Langstroth hive was the only types of hive we discussed. Moreover, we also only discussed the classic wooden 10 frame hive and its components. This left me very confused when I was left looking at bee company catalogs and seeing all of these different hive configurations and not knowing which one I should get. So I experimented and tried three types, each with its advantages and disadvantages.
There are two things every beekeeper should know; beekeeping is like gardening, you have to read and study to gain the knowledge, but you have to DO to gain the experience. Many times books will say this particular hive or bee works well in your area, but until you try and observe different outcomes, do you truly grow. For instance a book will not tell you the pollen sources within a 2 miles radius of you hive, the bees will.
The next thing a bee keeper needs to remember is that every bee keeper has an opinion. It is very hard to get two beekeepers in a room to agree on anything. Every beekeeper has their own microclimate where their hives are located, their own pollen source, and their own preferences. Therefore they will tell you their preferences, not particularly what would work best for you. Therefore you still need to experiment.
I have tried three different types of hives. I am still using all three types. For reference I live in Southern New England, winters can be tough and unpredictable. All of the beehives have the same pieces just different amounts. They both have two broad chambers (where the queen is and lays eggs), a honey super (where the workers store honey), a bottom board and an inner cover. The only difference is the material and the amount of frames.
The first hives I tried is the 8 frame wooden garden bee hive. They are called garden hives because they have a nice pitched roof to look pretty in the garden. Other than that, they are a normal hive. A beekeeper might select an 8 frame model over a 10 frame due to the weight of the hives. A full 10 frame honey super ready for harvest might weigh 60 lbs making it heavy for someone to lift. An 8 frame honey super might weigh 50 lbs. A disadvantage is that there is less space in the broad chamber for bee expansion, therefore it might get over crowded earlier than expected.
The 10 frame wooden hive is the classic beehive. It is made of pine (like the 8 frame wooden) and has enough room for 10 frames. The 10 frames make it a little bit heavier than the 8 frame to lift, but it allows plenty of room for expansion.
A beemax 10 frame hive is like the other beehives in design except instead of being made of pine, it is Styrofoam. The Styrofoam is actually hygienic for the bees, it is little, easier to assemble, works just as well of wooden hives. In New England I find the beemax hive to work very well because the Styrofoam acts as an insulator keeping the bees warm throughout winter (many owners of wooden hives insulate the hive in the winter by adding rigid foam board). However, during the summer there might be a humidity issue with these hives. Also the top cover of these hives is light, so you need to place a weight on them so they don’t blow off. Another disadvantage of these hives is the limit ability of them; there are only a few bee companies that sell them. Another disadvantage is the look of the hive. Many people, including my wife, do not like the look of the hive and would rather see the classic white wooden beehive.
I say experiment with different types of beehives. There are other types that I did not mention here. However, these are the three I have experience with and thought it would be beneficial to share.