If you’ve already decided on two characters, I’d imagine you have an idea of where Clark and (either) Iori fit best in your playstyle, and then you could figure out the remaining open position which might help narrowing down your choices. In any case:
K’ wont necessary end up using any HD combos if you put in on point and play well with him, and you could guarantee that your secondary character will come in with a Drive of a few bars. Otherwise the ‘hardest’ HD hitconfirm is starting from a cr.B cr.B st.B chain but you can play without that and only opt for starting with cl.C f.A or by spending a meter in the corner off a Second Shell launch.
He applies pressure pretty simply by having a good hopping air-to-ground j.D combined with his cancelable cr.B which if canceled into an Ein Trigger should net a knockdown or a launch in the corner. So he can set up to hop over sweeps or walk/run back in and pester with cr.Bs, and then mix up the timing on both options and land a cool footsie setup like delaying an Ein Trigger or doing a straight up tick throw. Granted that there’s a lot more to it than those two approaches–st.A can be used to preemptively AA the opponent from hopping out and can be followed with an instant Minute Spikes, K’ can wait and punish a roll or bait a desperation reversal, j.CD also works as a great air-to-ground and air-to-air, and neutral hopping with either creates a wall that the opponent can’t easily deal with without like DPing on reaction–but hopefully that helps you out a bit and there’s plenty of solid K’ footage from CafeID and good K’ play in 2002UM/XIII arcade (should you look to these, focus more on the general spacing and strategies rather than the specifics because obviously the finer points are completely different in XIII console/Climax). If you haven’t already, try using the C Ein Trigger for your pressure since it’s not as stiff on block and it comes out faster, but generally whenever you commit to an Ein Trigger you’re going to be more negative/neutral than from a cr.B so you’ve got to respect the situation sometimes and accept that your options afterward are more rigid/risky.
Takuma’s HD stuff isn’t that difficult except maybe for his most optimal corner carry. Honestly, his Drive Cancel loops have tighter links but really the main thing with all of Takuma’s combos is learning how to quickly charge* [db], f+D *immediately from a f.B. Even with basic stuff, he can do more than 40% from a clean hit/cross up/j.CD counterhit/command grab/anywhere juggle with just 1 meter and 1 drive, and honestly you’re probably better off capitalizing off every single possible instance with him anyway so you shouldn’t be fishing for HD when you’ve already earned a chance to use a Drive Cancel from an anywhere juggle or something, and plus his long-ass combos do hella damage anyway.
I’d agree with him being second or third, but some characters can hop his projectile and the recovery doesn’t allow him to trail behind his light projectile as well as other characters, so don’t expect to run a '98 zoning game with him but instead use it as poke or to force the opponent into the air where you’re ready to meet them with j.CD or anti-air with the C ranbu. His grounded normals are alright, but he can’t hitconfirm or rather create as much damage from an odd his like Mr. Karate can. However, his really low-to-ground hop arc and shockingly simple j.D and j.CD allow him to really be annoying on the offense, especially whenever crossing up with j.D (as usual, Takuma has cross up that’s as good as something you’d expect to see out of ST).
Andy’s floatier hop arc and limited aerial options contribute to one of his few weaknesses, but you can use it to your advantage with cross up j.D. And while you might not have seen a lot of HD from him, I know he has an easy corner carry and then a corner loop, both of which can be ended with NEO MAX for high damage. Even without that, Andy’s able to use Drive Cancels in the corner to do some surprisingly long juggles so the HD plays its biggest role midscreen where he doesn’t get too much damage from his other options. Otherwise all his tools and specials do what you’d expect them to do exceptionally well. As for bad matchups, all I can think of at the moment are characters that can meet him or out-play him in the zoning game or someone who can punish Zaneiken on block. So EX Iori fits the bill as an alright counter since he can EX DP to punish Zaneiken, meet him in a projectile fight, and stay on point with reaction DPs. I don’t think that matchup is as dumb as something like Kim vs Daimon though, where Daimon gets blown up by ff.A and air safe air overhead shenanigans and easy cross ups.
Applying pressure with EX Kyo should be easier than doing it with normal Kyo, for sure, since he has better light normals, less need to cancel into a command normal which can put in him a neutral or risky situation on block, and he’s got his Aragami rekka for safe frametraps, anti-airing, and poking/whiff punishing. Getting in might be an issue since j.D can be crouched under, but you can play it patient or look for a situation to roll or EX R.E.D. Kick your way in, or get into idea rekka poking range and go from there. In the lower and upper spectrums, his damage rivals Fireball Kyo and his HD damage isn’t spectacular (that, and the amount of tools available to him don’t greatly increase with meter) so I usually run him on point, netting 20-30% from lights or a rekka combo/anti-air/poke and in the corner it’s really easy to turn this into a hard knockdown into an easy safejump. If you don’t burn too much meter on him, you can pass it on to the next character or build enough for an easy HD combo into NEOMAX so take your pick.