Chris,
1) First off, good-on-you for asking questions / wishing to learn!
2) Allow me a quick preface, before addressing your specific questions?
I freely admit that I'm partial to more old school / classic ham rigs....and, I've personally known Bob Heil (who is now retired and no longer runs Heil Sound) for a few decades, and Heil Sound does make some nice mics (as does Electrovoice...I use a ~ 60 year old EV638 that I paid ~ $40 for, with my ~ 44 year old Drake TR-7).....
So, coming from me, this is an important preface:
a) Of all the "modern" rigs I've heard over the recent years (and, I've heard a lot), one of the best sounding / clearest transmit audio, is the Icom IC-7300 with its stock Icom hand mic (the HM-129)! Now, the '7300 itself is not my cup-of-tea, but I admit every one of them I've heard with the stock hand mic have sounded very good!
AND....and, with the stock mic or SM-30 desk mic, they've better than every other '7300, with ANY other mic, with ANY headset....fact is the stock Icom mic is one of the best mics for this rig! (fyi, getting decent aftermarket mics for Icom rigs has always been an issue....as the Icom stock mics have, for the past 30 some years, been great....and, this applies to the maritime/marine radios as well as their ham rigs)
Further, I've surprisingly heard quite a few IC-9700's on 2m FM, and I also must say that the one with some "headset" sounded over-deviated and all-in-all "crappy"....but every one of the other '9700's with the stock Icom mic, or the Icom SM-50 desk mic, have sounded great!
Of course, there are the "unknowns", such as whether those with headsets, and aftermarket mics, etc., have screwed-with their rig's transmit audio EQ, etc., where their mic gains and processor levels were set at, etc....but, these are also "unknowns" for all of the other rigs as well, so...
b) And, use caution with the FTdx-10...as Yaesu themselves states (in their manuals and marketing materials) that they use their ALC to boost the rig's talk power, etc. (Ugh!)
Goodness knows why/how these guys design their radios this way....but, I guess that's part of our "modern" amateur radio service.

So, make darn sure you grasp all of the transmit settings before messing with them....and this is especially true with modern Yaesu rigs (including the FTdx-10)....and, this means don't start setting things to some arbitrary number(s) that "some other ham" told you is best! (or even worse, don't make adjustments to get more meter deflection!)
Especially make sure your mic gain (and other settings) are adjusted so you have NO ALC deflection at all in normal speech (and even with a "raised voice", you should make sure you have no ALC indication / deflection), as these rigs are notorious for ALC pumping, etc. (causing buckshot splatter, etc.)
c) The audio amps in most ham rigs these days are pretty piss-poor, compared with stereo / hi-fi amps....they are not really designed to be used with the volume up higher than half-way....and, this also why using a good pair of communications headphones helps a LOT!
{Heck the audio amp in the original (multi-thousand-dollar) Elecraft K3 was so bad, everyone either was forced to use headphones, or they took a line level signal out and drove an external amp / speaker...}
So, while you're correct that the tiny internal speakers in many modern ham radios are fairly poor, their audio amps are, in some circumstances, equally at fault.
d) BTW, if your room acoustics are effecting your transmit audio, then your mic gain is up too high and your mic is too far away from your mouth! (this isn't "broadcasting")
And, while sure, room acoustics can effect your hearing of what signals are coming out of the radio's speaker, or external speaker....if this is the case, yes improving the room acoustics is great, but so is moving the speaker closer to your ears (and making sure it's pointing right at you)!
3) Next, I suggest you take a tiny step back from buying a new mic, headset, speakers, etc., and learn more about "communications audio" first.
Start with using the stock mics supplied with the radios; and a decent set of headphones...
I specifically recommend "communications" headphones, like the Kenwood HS-5, or a simple / inexpensive pair of headphones, no need to spend hundreds of dollars here! As for "speakers", while the radio manufacturer's "matching speakers" are usually good (some are quite good, some just "okay"), and I myself use both my Drake MS-7 and (shh, don't tell anyone) I also use a big Yaesu SP-2000 (with aftermarket acoustic insulation inside), and both are good, but the big SP-2000 is very good...(fyi, I got a GREAT deal on a used SP-2000, that I just could not pass up!)
But, they are damned expensive for what you get (the cost is mostly just to "match" the radio), so...many hams use simple home stereo "bookshelf" speakers or computer speakers, to good success....and, they are
much less expensive!

As Mike, WA3SKN (and the others), points out there is a world of difference between our HF-SSB "communications audio" and hi-fi / music / multi-octave-singing audio!
As you can see from these graphs from my QRZ page, the human speaking voice (especially "raised" or "loud") has fairly narrow range and peaks....with vowels being the lower audio freqs that are naturally louder, and much of the hard consonants (where most specific comprehension and annunciation is primarily transmitted) being above 1000hz (approx 1250hz - 2500hz):

This the primary reason I recommend using the stock mic(s) and simple speaker(s) and headphones! (at least for now)
FYI, a decent pair of headphones (even cheap ones) can make a world of difference in picking signals out of the noise!
The more you use an HF radio "clean" (that's without DNR, etc.), with a good set of headphones....the more you'll realize the best "analog signal processor" is inside your own head, and is usually better than the "digital signal processor" in the radio.... Hi hi.

{I'm speaking figuratively here}
4) Also, like some of the others here, I'm wondering what type of operating you're doing / planning on doing?
'Cuz, using a "headset" for casual operating is going to "get old", real fast....(translate that to: "for a contest, they're great....for most other operating, they're a pain-in-the-ass")
Perhaps, reading about microphones / headsets a bit less....and get-on-the-air more....might allow you to see that while, in some weird circles, it's considered "cool" to use aftermarket mics/headsets, etc., but for anything but contesting (especially multi-multi), or some other small niche, a headset is a pain....and, while some aftermarket mics are good, especially if on "booms", etc., most find that (again, except for contesting or serious SSB DX'ing) the manufacturer's stock mic to be good (and in the case of Icom and Kenwood, very good!)
5) You asked for manufacturer's model numbers....so, here goes:
a) For your Icom IC-7300 and IC-9700:
1- The Icom HM-129 hand mic (this is the stock hand mic)
2- The Icom SM-30 (or SM-50) desk mic
The "matching speakers", SP-23 or SP-38, are good...but pricey! (I enjoy having a nice speaker with a front panel headphone jack, so the pricey SP-38 is good for this)
Or, just about any decent "bookshelf" stereo speaker....
Kenwood HS-5 headphones (or if you prefer lighter-weight phones, the HS-6 are very good as well)....fyi, I own both and love them, both.
b) For your FTdx-10:
1- The Yaesu SSM-75e hand mic (this is the stock hand mic, I think?)
2- The M-1 (or M-100 ) desk mic
The "matching speakers", SP-30 or SP-2000, are good...but pricey! (I enjoy having a nice speaker with a front panel headphone jack, so the pricey SP-2000 is good for this, as well as it does have very good sound, no rattling, no "tinny" / crappy sound!)
Or, just about any decent "bookshelf" stereo speaker....
Kenwood HS-5 headphones (or if you prefer lighter-weight phones, the HS-6 are very good as well)....fyi, I own both and love them, both.
6) Finally, if your hearing is really bad (you need to turn the radio's volume up 3/4 of the way), then I suggest using a line-level out of the radio (or a headphone out), and drive an external audio amp and speaker....(or just use the Kenwood headphones)
As I wrote above, the audio amps in our radios are NOT designed to be run much higher than half-way up.
Heck, I've seen specs of "10% THD at 1-watt" or "10% THD at 2 watts", etc....and, the old Elecraft K3 was even worse!
So, if you need high-volume levels, use an external amp/speaker, or good headphones (not a headset).
I really hope this helps....but, to be honest, you've gotten the cart well ahead of the horse here, so I highly recommend you push the whole "headset" and "aftermarket mic" ideas back onto the back-burner for a while.
73,
John, KA4WJA
P.S. While some ham rigs can have slightly wider transmit (and receive) audio passbands than the "ham standard" of ~ 2.3khz to ~ 2.7khz, remember the "telco" standard has been 2.7khz (300hz to 3000hz) for many decades (used-to-be 300hz to 3100hz, which is still the commercial SSB standard).
Most ham rigs these days are ~ 2.4 to 2.7khz....my old TR-7 is 2.3khz (transmit and receive), and while everyone comments on the "great audio"....when I'm on-the-air with my friends with ANAN's, etc. where they're ~ 3khz, in comparison they say my audio is "communications grade" (which to me is a compliment, but to a "broadcaster" is an insult)
Just saying, whether it's a mic, headset, speaker, and/or headphones....even the "wider" guys are limited to "communications grade" audio, so the search for "better audio" should be about reducing the noise and distortions, not about bandwidth!