I have found both of these cameras in a really good kit for $1200. I was wondering which one would work best? I also heard rumors of a D80x or D90 coming out soon. Do you think I should just wait for those or jump on one of these deals?

Except for the sensor cleaning ability the D80 is better. Yes there are rumors of the D90 but no one seems to know what the upgrades will be.
What are the kits and where from? A lot of kits give you stuff you end up having to replace and definitly read our dealer feedback forum before buying anywhere.

One is from Cameta's Ebay site and the other is from Canoga.
D60: http://www.amazon.com/Nikon-Digital-18-55mm-55-200mm-Accessory/dp/B00155137S/ref=pd_bbs_sr_3?ie=UTF8&s=electronics&qid=1210757355&sr=8-3
D80: http://www.canogacamera.com/detail.aspx?ID=42405

Both trusted dealers. I think you are getting better glass with the d60 deal but I don't know much about the sigma lens.
The other stuff in the kits is just that.....stuff. Yeah you'll need a cleaning kit but they're inexpensive and the case won't meet your needs as soon as your kit begins to grow.
Card readers are cheap.
I don't know what your budget is but if I were starting over,(I do have the d80), I'd look for a kit with the 18-200 vr which I don't have but wish I did. Its a very good walk around lens and then when you've got some experience under your belt and discover your shooting style/passion you'll know what other lenses you want/need/can't live without.
I did find this which seems tempting http://www.canogacamera.com/detail.aspx?ID=38093 but I don't know how well the Sigma compares with the Nikon lens except that its much less expensive. I found reviews which were positive but no comparisons.

I just picked this kit up last week from Cameta. I went with the refurbished camera and lenses but I cant tell this camera was used. Not a mark or blemish on it. I payed for the extra shipping and it was here on Wed and I placed the order on Monday. Love the camera and am very happy I left the Olympus E500 behind me.

http://www.amazon.com/Nikon-D80-3-5-5-6G-55-200mm-Refurbished/dp/B000N6KUCE/ref=sr_1_72?ie=UTF8&m=A36DL6WLK2RE7O&s=electronics&qid=1211057465&sr=1-72