I need your help on which type of speakers to buy for the room space I have available, its a room with these measurements: 8.40ft height, 12.30ft width and 21ft depth.
The following is just my opinion.
The room dimension which is most significant in this case is the width, because the distance from speakers to sidewalls is relatively short, assuming the speakers will be on the short wall.
Early sidewall reflections are a two-edged sword: They increase the width of the soundstage, but can decrease image precision and image depth (and can cause coloration if they have a significantly different spectral balance from the direct sound). So there is a juggling of tradeoffs: Do you prefer a wider soundstage, or a bit more precise and a bit deeper soundstage?
If you prefer a wider soundstage, you might use a little bit of diffusion at the first sidewall reflection areas, and maybe minimal absorption as a last resort if the sound is too bright.
If you prefer "a bit more precise and a bit deeper soundstage", there are several things you can do to address the early sidewall reflections: Reflect them away from the primary listening area using large flat angled surfaces; diffuse them; absorb them (not my first choice); and minimize them via loudspeaker radiation pattern and speaker set-up.
Since you're asking primarily about loudspeaker types, I won't go further into room acoustics.
In general a wide-pattern speaker, whose off-axis energy is smooth (i.e. it sounds like the direct sound), is a good choice for the widened soundstage approach. Examples might include the three- and four-way Revels, as Revel pays a lot of attention to getting the off-axis sound right. An omnidirectional speaker might make sense if you want to go really far in this direction. I'm tossing these thoughts out without having much of a feel for your price range.
If you prefer precision and soundstage depth, then imo you want speakers with a fairly narrow radiation pattern. Horns and planars come to mind. Note that planars will sound best with at least five feet between them and the "front" wall, such that the arrival of the reflected backwave is delayed about 10 milliseconds by the path length. Dipoles have a null to the side so when you space them wide apart and toe them in fairly aggressively, they have relatively little early sidewall interaction.
If the sweet spot is just for one person, you might consider the Sanders Sound flat-panel electrostatic loudspeakers. Tiny sweet spot but magnificent imaging and articulation for one.
If you want a wide sweet spot, horn speakers aimed such that their axes criss-cross in front of the listening area are a possibility. The JBL 4367 comes to mind. Also omnis give a wide sweet spot.
I have not talked about speaker "voicing" because within these different loudspeaker types there are different voicings to choose from.
How the loudspeaker's radiation pattern interacts with your room is of course not the only consideration, but if you have strong preferences regarding soundstaging and/or sweet spot width, imo it's worth taking into account.
Note that the one thing I believe to consistently matter is, that the speaker's reflections sound like the direct sound. Which implies that the radiation pattern be smooth over most of the spectrum, or at least over something like 1 kHz to 8 kHz. This will avoid the reflections significantly coloring the sound, because they will be supporting the first-arrival sound rather than fighting against it.
An example of what is imo NOT the kind of speaker you want, unless you plan to hire an acoustician, would be a two-way with a 6" midwoofer and 1" dome tweeter. What typically happens with such a speaker is this: There is a significant discontinuity in the off-axis energy in the crossover region, as we transition from the 6" midwoofer (which is beaming somewhat) to the 1" tweeter (whose pattern is very wide because the wavelengths are long relative to the diameter of the dome). We end up with excess off-axis energy at the bottom end of the tweeter's range, typically 2-4 kHz or so. This just happens to be the region where the ear is most sensitive, so when that excess off-axis energy arrives as reflections, it can result in a forward sound, or even harshness and/or listening fatigue. (There are voicing techniques for mitigating this effect, but they involve tradeoffs.)
Feel free to ignore any or all of this if you feel it's not applicable.
Best of luck in your quest!