Is there a different upper for the .223 or the 5.56 or does that just depend on what barrel is used?  Also, what is an average parts kit cost to assemble a stripped upper?  Thanks!

Just depends on the chamber/barrel.

I haven't really heard of an "upper parts kit".  I think you'll have to buy the parts individually if you already have a stripped upper.

I suppose prices can vary depending on what individual parts are ordered.  About what could I expect to pay for the parts to assemble an upper?  I am looking for good reliable parts, not the best or worst.  I am mainly doing this for the experience I'll gain, but will I be saving much money?

Well,

Not including the B/BC and the barrel assembly, you are looking at:

ejection port parts $6
forward assist parts $12-$13
charging handle parts $13.50-$15

places to check out
www.rbprecision.com
www.georgiaprecision.com
www.adcofirearms.com

Here's what you'll need and the prices:

barrel assembly (with front sight base, handguard cap and barrel nut)     $200*
gas tube and pin    $9
delta ring kit     $10
ejection port cover assembly   $6.50
forward assist kit     $11.75
bolt carrier group     $110
charging handle     $17

Total:   $364

*The biggest variable is the barrel.  Price will depend on length, type, pre or postban, and if chrome-lined.
These prices are off of Rock River Arms' website, and you should expect to pay less, especially with the dealers over in the EE.  For example, one of them has a sale on the bolt carrier group and charging handle together for $112 shipped.  IMO, RRA parts are a good balance between cost and quality.