Hi Robert; You are correct in that you do not have to use a barrel.
Using brick instead is called a brick bell. Quite a bit larger than a barrel but much more ascetically pleasing to look at.
And no pipes thru a solid heavy mass.
Yes, you could cover it in cob if you wanted.
Spend some time looking at posts here at Permies.
You will see examples of both, brick bells as well as a barrel and piped mass
RMh's
There are traditional J tube rockets as well as the newer stronger batchbox designs.
Check it all out then come on back and ask questions.
We have a whole crew of happy rocket scientists eagerly awaiting your questions!
But don't wait to long or our group of rocket scientists could be "too happy"...