Memory and Video Cards

Alright I need some help with a few things.
I plan on upgrading my rig in preparation for BF4 and future games to come.

Right now I have a ATI Raedon HD 6770 video card. I run BF4 with minor lag.
I also have 6GB of memory, however some of the memory sticks are old and from an older computer.

I was wondering is it smarter to upgrade my card to this: XFX Double D FX-787A-CDFC Radeon HD 7870 GHz Edition 2GB 256-bit GDDR5 PCI Express 3.0 x16 HDCP Ready CrossFireX Support Video Card - Newegg.com
And then also, I have never bought memory before, I have no idea how to go about it.

Which of these would you prefer?

Corsair
CORSAIR Vengeance 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model CMZ8GX3M2A1600C9 - Newegg.com - 2x4GB = 8GB = $93.99
Newegg.com - CORSAIR Vengeance Pro 16GB (2 x 8GB) 240-Pin DDR3 SDRAM DDR3 1866 Desktop Memory Model CMY16GX3M2A1866C9B (Blue) - 2x8GB = 16GB =$164.99
or
Kingston
Kingston HyperX 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model KHX1600C9D3K2/8GX - Newegg.com - 2x4GB = 8GB = $85.99

or is there something out there that's better? I really just want 8GB but the 16GB seemed like a deal with Corsair.

You probably wont need more than 8gb of ram.

Corsair, and Kingston are two of the best so its hard to pick.

The 7870's seem pretty solid, I want to get my hands on a 7970.

My laptop uses 16GB of 1600Mhz DDR3 Gskill RAM and I've never had any RAM problems. I sometimes hit 8GB worth of processes, however, 8GB or 12GB should suffice. I'd run Adobe After Effects, Photoshop, and Planetside 2 at the same time to get those numbers and you shouldn't be doing that anyways. Go with Corsair, Kingston, or Gskill for RAM. The 7870 should be a pretty solid upgrade for you but you should really take your processor into as much if not more consideration than your video card. AMD FX-8350 Vishera is always a good choice. BF4 doesn't seem to be particularly intensive with graphics so much as processing, so...

Go for atleast 16 GB if you can afford it. Otherwise stick with 8.