What is a mid length (16)? What is full lenght?  If the Eotech55 is to the M4 what is to the ar10? What is the component that the dot sight fits on? For instance Eotech or aimpoint. When I buy an AR will I have to buy that part? Should I buy the AR10 with an ACOG or Ar15 with and ETech?
The hand gaurd replacement with all the rails on it and the hand grip, what is the name of that product?

What do you suggest?
I want an ar 10 or 15 don't really matter just want a fun range gun. Now I want to be able to defend myself with it if neccesary. Meaning I won't be deer hunting with it. What do you think is the best setup for me.. I was thinking the M4 but with all them parts, I just want to buy it ready to go, so whatever you suggest be specific so that I can purchase it all at once. Thank You all for your time.

178 posts?  Where have you been posting?  Anywho, AR10 isa .308.  For a fun range gun an AR15 in .223 would be better.  The part the optic attach to is the upper receiver.  You can't have a gun w/o the upper receiver, so if you want the picatinny rail, just get a flat top model.  Hand guard is just as you know it, a hand guard.  Just read through here and learn.  If you want one ready to go, just buy a complete rifle and have it shipped to your FFL.  BTW, Full length = rifle length.  Then you have carbine length and in the middle you have your middies.  They refer to the length of the gas tubes that run along the top of the bbl.  Hope it helps.

Thanks.  Any other suggestion?

Midlength and Full length refer to the gas systems- the distance between the upper receiver and the gas block.  For Carbine Gas Systems, it's about 7 inches, Midlenth Gas Systems 9 inches and Rifle or Full Length Gas System around 12 inches.

The size of the gas system can be independent of the barrel length to a certain degree.  

The size of the gas system will determine what handguards you use- standard hanguards attach at the delta ring in front of the upper receiver and at the handguard cap at the gas block- the triangular tower near the front with the front sight in the top.

You can use an Eotech on any AR15 or AR10 as long as you find a way to mount it- either on a flattop upper receiver or a mount connected to a carry handle or last but not least, on a securely mounted handguard which brings up one of your next questions...

The best way to mount a grip up on the front handguards is to get a railed forend that replaces the standard plastic set.  They are usually between $100 and $350 depending on size and manufacturer.  Some are simple DIY and some are not so simple.  

You can use an Eotech or an Aimpoint, whichever you prefer.  When someone has an Eotech mounted on their rifle, they could just as easily use an Aimpoint- they are non magnified and mount on picatinny rails.  Aimpoints require a mounting with a 30mm ring while Eotechs can be purchased and mounted without buying additional parts.

ACOGS are a different animal.  They are magnified scopes and need to be mouned in a certain spot on your upper receiver.  As long as you get a flat top, you will be ok.

AR10s are more expensive than AR15s.  They aren't as cheap to shoot and there isn't as many fun toys for them.

I'd suggest a 16" midlength from RRA as a good place to start.  Get a chrome lined barrel and a flattop receiver with a removable carry handle.  But the Aimpoint or Eotech later.

This is my midlength with 16" barrel and it's carry handle sight:


Here it is with an Aimpoint: