My rig

I have a:
MSI 970A-G46
AMD FX8350 Clocked at 4.2Ghz
8GB Ram (unknown as of right now)
old school HDD (I know I need to upgrade this)
MSI 660 Twin Frozr OC Edition

Any advice on what I really should do besides getting an ssd for my windows and use the HDD for storage?

Your weakest link is your hard drive for sure. Grab a nice 120gb for windows and select games/programs, or better yet a 240gb to cover a better swath of things you like to use and use the HDD for storage.

SSD is ALWAYS the number one upgrade.  Its insane how big a boost you get.

After that…what do you use the rig for?  Gaming...upgrade the video card (what is your budget?).  Surfing and the such....dont bother beyond the SSD.  Its more than enough for day to day.  Save your pennies and build a new rig...and simply re-use the SSD.  For SSDs...hard to beat the (oldie but goodie) Intel 520, Crucial M550, Samsung 840Pro, SanDisk Extreme 2, Corsair Neutron GTX....anyone of these are great kit.  😉

Agreed on the SSD drive for Windows & most used/performance critical stuff.

My friend PC use a old PATA 160G HDD (and not even the black WD performance edition, but blue mediocre one) and just stepping down from 500G PATA WD Black HDD feels like the computer is draging a lead brick or two around. It just suxx. So ancient HDDs are first to dump.

The rest depend on your budget and goals. GTX 660 is not that bad card, after all. With reasonable settings (no high or ultra, no no) it can go well in almost every game. And actually it is a well balanced to the used CPU. If you add much faster graphic (think 780ti or 290X), then you will be CPU limited in most, if not all, cases.
Only one thing you can benefit in terms of GFX card - use AMD one. On slower PCs, the Mantle give as much, as almost 50% faster framerates. So a AMD card will help you big time, even with current CPU, if the game you play most utilize (or at least plan to) Mantle. Like BF4…
If not, then you did not benefit much from GFX upgrade anyway, so it will be doubtfull, if is not better to start saving for completely new rig, if you need more power/fps in games.