I have a slab side barreled upper with a duckbill suppressor and a 12 right behind the suppressor. I have had it for years and I'm assuming it would be the correct barrel for a 602 build. Did all 602's come with a chrome bolt and carrier?

I also have two new barrels marked C MP C. Are these the correct barrels for a 603 build? They are complete except for the gas tube and weld spring. I think the spring is the same as a current one, but did the gas tube have a different bend in it back then?

Your barrel sounds like it would be correct for a 602. My 602 barrel (that I bought as a barreled upper w/a 602 receiver) has the same 12 marking by the FH, about 1" from it. Does it have a cast FSB? A cast FSB will have the word "up" & the arrow raised above the surface. Look in the M16 variation guide for a good pic of a cast FSB.

You should be able to find more answers to your questions here:
Retro Black Rifle
Just click the box on the left that says "Military Rifles", then click the model number your looking for.

More info here:
Colt's USGI M16 series variation guide edition IV

Post pictures of your upper, it will be easier to tell what you have.

As far as the " C MP C" marked barrels being correct for a 603, I do not know, but the first link I provided should help you decide which model they are correct for. The weld spring is the same for all models, & you are correct about the gas tube being different, but I'm not sure when it was changed to the new style. FWIW though my 602 upper had the old style gas tube on it.

Quoted: I have a slab side barreled upper with a duckbill suppressor and a 12 right behind the suppressor. I have had it for years and I'm assuming it would be the correct barrel for a 602 build. Did all 602's come with a chrome bolt and carrier? I also have two new barrels marked C MP C. Are these the correct barrels for a 603 build? They are complete except for the gas tube and weld spring. I think the spring is the same as a current one, but did the gas tube have a different bend in it back then?

The upper your describing sounds like it will make a great 602 clone. If you want to know if it's from a 602 originally you should check out Ekie's tacked thread at the top of the Retro Forum Page HERE. He's got great photos and info on Colt barrels there. Also a 602 upper will have an engraved arrow and R above the windage drum not embossed like later 604 slickside uppers. Yes, 602 has chrome carrier and bolt.
You'll also find the answers to your C MP C barrel questions there

ETA: +1 on what HK45 said

Quoted: I also have two new barrels marked C MP C. Are these the correct barrels for a 603 build?

The 603 covered a lot of territory, development wise.  A 1976 M16A1 was a changed gun from a 1964 XM16E1, but both are Colt model 603.

The C MP C marking puts it around 1971 or so, a not-quite-late model M16A1.