The TL;DR answer is: the gloves. Specifically the heroic Aldriana's Gloves of Secrecy, which drop from Rotface. That's the optimal choice - but there are other decisions you face. More of those at the end.
This is all based on the heroic levels of gearing. That's the long haul. In the short haul things aren't so different, honestly, but you might as well invest in what you're going to hope is the best of the best, right? Thought so :)
First, the heads. We have the T10 head, the lovely discarded bag of entrails from heroic 10-man, and the geistlord punishment sack.
The difference between the T10 and the entrails is (in favor of the T10) 29 agi, 72 stam, 114 crit and 6 arpen at the cost of 34 ap and 92 haste. That's a clear win.
The difference between the T10 and the Geistlord is 24 agi, 106 arpen at the cost of 48 ap, 8 crit and 98 hit. Another big win for T10; arpen beats hit, and you're not hurting for that much hit most of the time.
Next, the T10 chest vs. the Ikfirus' sack of wonder (which is BoE on normal mode!) and the Chestguard of the Frigid Noose (another 10-man heroic drop)
T10 chest vs Sack of Wonder: 16 agi, 122 crit, 106 arpen vs 16 AP, 114 hit and 106 expertise, and an extra blue socket. This is close, but arpen and crit are more valuable than hit and expertise, even with that additional socket. Still, consider this if you're gearing up your cat and bear; you can use this as a double duty piece and be pretty happy.
T10 chest vs Chestguard of the Frigid Noose: 33 agi, 76 stam, 122 crit, 15 arpen vs 16 AP and 111 haste. The agi and crit overwhelms the haste here.
Next is are the T10 shoulders vs Cultist's Bloodsoaked Shoulderpads and Skinned Whelp Shoulders (10-man).
T10 vs Cultist: 8 agi, 82 arpen vs 74 haste and a yellow socket. The arpen works out best here.
T10 vs Skinned Whelp: 32 agi, 44 stam, 26 crit, 2 arpen vs 18 AP and a red socket. The 32 agi alone wins here.
T10 legs vs Gangrenous Leggings: 16 agi, 122 arpen, 106 expertise vs 16 ap, 122 crit and 98 hit and a blue socket. This normally would go to the Gangrenous, save that hit is a lot easier to get than expertise and arpen beats the hell out of crit. The socket is awful tempting though.
T10 legs vs. Ivory-Inlaid leggings: 45 agi, 41 stam, 51 arpen and 106 expertise vs 20 AP, 116 crit and a red socket. Mostly easy choice.
T10 vs Aldriana's: 8 agi, 8 haste vs a yellow socket. Finally a clear winner.
T10 vs Scourge Stranglers: 16 agi, 50 stam, 10 AP, 18 arpen, 82 haste vs 72 crit and a yellow socket. Not even close, especially given how good haste is now.
So the answer is the gloves, right? Well...maybe. If you're gearing for bears and cats, it might be a better choice to go with the chest instead. The difference between the T10 gloves and the offtier piece is really fairly small (8 agi/haste vs a socket), but the cost in badges is much greater for the chest. Plus, having the chest means you have the best in slot for a bear AND close to the best for a cat, depending on your hit/expertise levels. The disadvantage there is that just with the T10 legs and the Sack of Wonder, you're going to be over the expertise cap by 80 points! Ugh. And since you desperately want 4pT10, going with an offtier piece in the legs isn't an option.
Plus, honestly - you're going to have hit around too, so it doesn't do as well for you.
Still - if you have to make a choice for gearing up both, that's not a bad one. Another option is to try and make the chest and gloves your 'shared' pieces, which means your offtier can be one of head, legs and shoulders. Given the expense and the relative difference in value, I'd probably go with the Gangrenous legs as my offset piece in that situation for one spec and possibly the Geistlord punishment sack for the other. That means you'd be buying two sets of shoulders, one leg and one head, which isn't so bad at the end of the day.
As always - make an informed choice based on your gearing values right now. If you know you're not going to ever do heroic 25-man or get a token, that may change things significantly. Don't not get upgrades in slots just because you'll get rid of them at some point too; even if you spend your emblems of frost on nothing but tier pieces, you're still looking at about 8 weeks before you can get 4 of your 5 pieces. This assumes that you're spending 65 on the shoulders and hands and 90 on the legs and head - it's actually more for a cat if you're going for the chest (345, to be precise). Assuming you've done every heroic daily, the raid weekly, and run 10-man and 25-man content and have done the new quests, you're looking at 41+35+35+35 = 146 badges when the next gate is unlocked. Assuming that's three weeks with three new bosses, you're looking at a weekly gain of (5+14+14+14) = 47 badges, or another 141 over those three weeks. Assuming another 3 bosses come out for three weeks after that, you're looking at (5+14+20+20) = 59 badges for those three weeks, or 177.
Or another way to put it: if you do everything - you'll get 4 pieces including the expensive ones at the end of the 8th week.
So...don't splurge on other bits. Don't get the offtier pieces that are available. Don't buy primordial saronite. Unless, of course, you can wait for all this - then you should gouge suckers trying to get their shadowmourne. :)