im confused... you would want to wear mithril full plate. you keep your move speed. then use what ever shield you want to make sure it is also mithril.
The ACP effects taking 10/20. All it means to take X is that you use X instead of rolling a d20.
As for a good target number on acrobatics, consider the penalties and bonuses. Assuming a 22 Dex and 15 ranks in acrobatics (trained), you'd have 6 + 15 + 3 = 24. Taking 20 would give you 44.
40 lets you walk up a 1" wide ice-covered beam set at a 45 degree angle during an earthquake. That's about as crazy as I could make it. It lets you clear 8 squares (40 feet) with a running start, or 4 squares from standstill. Lets you clear 11 feet with a vertical jump with running start or 5 feet from stand still.
The more important thing is to tumble. The DC to tumble through a threatened area (thus avoiding the AOO) is equal to the CMD of the bad guy threatening that square. This is at half speed; to do it at full speed, add 10 to the DC. If you want to tumble through a monster's square, add another 5.
So if you have a 44, you can tumble through a monster's square at full speed only if the monster has CMD <= 29, but 39 if you move at half speed.
I'd say 40 is the upper bounds if you want to pursue god-like tumbling ability, which is to say DEX + Level + Training Bonus - ACP = 20 would be a good max to consider. I also suggest Mithral armor of any kind in order to pull this off. I would say stay away from heavy armor since it would cost you 10 feet in movement.
Just for clarification, your armor check penalty applies to your Acrobatics modifier, even when taking 10 or 20. Since the mobile fighter keeps Armor Training 1 and 2 this penalty is reduced by 2.
As for what's "best," it would depend on the particular build and what you are trying to do. All things being the same, I would either go with
-- If I have a higher Dexterity modifier than +3, a magic breastplate. After Armor Training 2 and masterwork improvements, the ACP is only -1, and my max Dex bonus, after Armor Training 2, will be +5. (Mithral breastplate will eliminate the penalty entirely but may not be worth the cost depending on what you want to do). If you get an Agile Breastplate (APG) you can also then reduce your ACP to 0 for using Acrobatics to jump.
-- If my Dexterity modifier is 3 or less, I would consider magic mithral full plate. Mithral + armor training also reduces the ACP to -1 in this case, and it being Mithral it counts as medium armor for movement, so your speed does not decrease even though you do not have Armor Training 3. But your Max Dex will be +3.
In either case, any magic light shield or a mithral heavy shield will do for a shield bonus. My preference would be the light shield, personally, just to go with the lighter fighting style theme.
Optimally at high levels, you'd want a 2H reach weapon, Whirlwind Attack, and Lunge. And just run around out of enemies' reach attacking everybody w/ WWA thanks to the level 11 class feature (WWA is a full attack action, it works). Combine with Dazing Assault for more fun.
And yeah, you eventually want mithral full plate. You should not be making a dex-based attacker, just keep dex reasonably good instead of min-maxing the hell out of strength so you can get the most out of the mithral full plate's max dex bonus (+5 for you; a 20 dex with a +4 item is not too hard to achieve while having str as your best stat).
You also need to ensure your DM allows you to use Gloves of Dueling, or else I'd reconsider the archetype.