If you're going Inspiring Commander and looking at multiclassing, I'll share a build that is similar to one actually actively being played at my table.
Race: Elf
Primary Stats: Int, Con, Str, Dex, Wis, Cha from highest to lowest
Build:
Five levels gets you where to need to be to get Inspiring Voice, which is bread and butter of this archetype. It's basically built front-loaded to be worth taking up to 5th level and then multiclassing or prestige out into something interesting.
The reason for taking Elf as your race is this archetype. If your DM allows it, other races could be used however. This magus archetype is built for multiclassing, and one of the best ways to gain a big bunch of bonus feats. Consider taking this to 5th level to give us 2nd level spells and the free 5th level combat feat, though you might want to only take a 1 level splash instead for just the bonus feats and 1st level magus spells. The losses from the archetype for armor proficiency mean nothing to us since we already gain them back from Inspiring Commander. Net gain is an Exotic Weapon Proficiency, Combat Expertise and Dodge. Arcane Augmentation is actually fairly useful too, granting you a +5 bonus to a lot of skills you normally wouldn't spend many points into.
A two level dip into this class is the reason we took at least one level of Spire Defender. If you're an Elf, the Forlorn alternate racial trait will mean your feat prerequisites are essentially nothing, since they all came from bonus feats. Two levels here give you Int to your AC, which if you're playing as an Int focused build will be an extra +6 or higher on average. You could continue here if you wish, though the remainder of the class is somewhat unimpressive.
Another two level dip prestige, mainly for the bonus to Aid Another. Yes, this stacks with Inspiring Commander's abilities. This class stacks for your Bardic Performance levels too, grants you the ability to reroll a d20 once per day, and a bonus to saving throws on charms and compulsions. All for the low cost of a feat you'd probably want anyway, and a few skill ranks that aren't too tough with an Int focused build.
Cheap entry requirements, and a free immunity to any fear effects, plus a bonus on the first round of combat. Assuming your DM isn't too strict about the flavor prerequisite, one level spent here isn't a bad option. Two levels might be worth the reduction in AC penalty during a charge and reroll on saves, but probably not.
Yes, per the rules this should allow you to stack double your bonus for Inspire Courage on yourself, even with Inspiring Commander, and the levels should stack. Best check with your DM though, it's an odd one.
The whole point of the Inspiring Commander, it gives us a lot of new ways to use our Bardic Performance. Check with your DM, but Inspiring Commander should change this to let you use it 4+Int instead of Cha times per day. As many levels as you want in this class is a good idea once you've got everything else you want.
Bardic Performance won't stack, unfortunately.
If it was me, I would probably run Order of the Dragon and get to the Strategy ability ASAP. Standard action to grant all allies an immediate action move once during a combat is insanely good. They (and you) start a battle by running circles around the enemy. Enemy goes first and attacks? Nope, immediate move away from the attacker into five-foot-step range. Ally goes first? Immediate action to move up, then full attack. Your second turn comes around? Immediate action to move up and full attack. Etc.
Delaying levels also delays Bardic Performance from becoming better and easier to use and delays Challenge as well. Personally, I wouldn't dip more than 1 level, at least early on.
Edit: if stacking Challenge, Order of the Dragon and Inspire Courage you have a huge bonus to weapon attack and damage... Going two-weapon would really stack up the effects. Like using two longswords or rapiers (with Effortless Lace to avoid the -4 penalty). There are tricks to make it easier to do TWF stats-wise while keeping decent strength.
Order of the Dragon grants you an attack bonus against targets you threaten and the ability to pseudo-pounce with immediate action move once per battle. "You are your own ally" according to Paizo, and you benefit from your strategic skill like anyone else in this case. Both of these benefits are extremely useful, especially for a Cavalier. Getting an immediate action move means that even if you get left behind on turn 1 while using your abilities, you can jump right up into the front line with a full attack on turn 2.
If you have a level of Dawn Bard, you have level 1 "battle dance" that works as it says. It has no crossover with "inspiring commands", because they are two different abilities from two different classes that work differently.
As far as getting TWF goes, you can get it with DEX normally, or with INT if you take Artful Dodge. If using INT, it's easy to boost with a headband (unlike DEX, where you want a STR belt instead). Either way, a racial bonus makes it pretty easy - including Dual Talent Human that can grab +2 to both STR and DEX. Something like 15/17, 15/17, 14, 12, 10, 9, or 16/18, 12, 14, 14/16, 10, 8, is easy with dual talent, though dual talent isn't necessary. Chain Challenge won't grant more than one extra challenge without at least 14CHA and Inspiring Commander is INT based.
Student of War vs. Duelist
1. Duelist is very much a Dex focused prestige. If you're taking Power Attack at 1st level, it's likely you're planning to focus on one handed weapon group, not light weapons. Essentially this means either Power Attack is giving you diminished returns, or you're gonna fail to have enough points to get the Dex score needed to get Mobility as a prerequisite for Duelist.
2. You only gain +1 AC per level in Duelist. You'd need to sink at least 6+ levels into this class to equal what you gain in 2 levels with Student of War.
That's not to say Duelist isn't a good option to consider. In fact, if you did both Duelist and Student of War, you get to double-dip your Int to AC. However remember that Student of War replaces your Dex with your Int, not adds. It means you lose significantly if you have a high Dex, which is almost a mandatory high stat for entering Duelist. Student of War works best when you have an Int of 18+ but a Dex of 8.
The single biggest draw of Battle Herald is that you can continue your Bard performance stuff on a more martial character with full BAB. If you've got a 3rd party Cavalier that already has full-on performance, I'm not sure why you would use Battle Herald. Perhaps people don't realize that Inspire Courage and the Battle Herald abilities that add attack and damage are both competence bonuses, and don't stack?
There are all kinds of 1-level Will save dips, though Saving Finale is definitely nice.
Note that things requiring immediate actions may be tricky. Challenge and Chain Challenge run on swift/immediate (which is partly why I wouldn't bother cranking Chain Challenge beyond x1), and other Cavalier abilities also may well do so.
One level of Medium to summon a Champion spirit is always a nice bonus. Easy damage bump, including some to allies, and some extra tricks.