What are your goals and expected outcomes for building the barrel? Your goals and expectations greatly influence the project requirements.
In order of importance the biggest factors influencing the project will be:
Goal learn to build barrel or produce a 1000 yard champion barrel?
The Operator Knowledge, Skill, Attitude/Aptitude, training qualifications and certifications. Are you a master machinist or a novice? Are you a gunsmith or a weekend shooter? Do you understand the importance of the crown and which shapes are best under various conditions?
Machine capability what is the concentricity run-out of your equipment and for what length of work can your equipment hold that tolerance? Is the length of the barrel within that working tolerance? When building a barrel, it will experience all the potential motions of a plane; pitch, roll and yaw. Machine variances on those axes will affect barrel quality. How many locking points does your lathe use? What is the repeatability capability of the machinery? Do you plan to use cut or button rifling?
Without knowing anything about your goal, skills and equipment providing more detailed answer is difficult.
Suffice it to say that the greater the accuracy requirement of the barrel, the greater the accuracy of the equipment used to produce it. More accurate machines are much more expensive. If you have the money to buy the best then you are ahead of the game. CNC machining takes much of the human error out of the machining process and allows for greater repeatability capability, but adds to the complexity by requiring programming.
With all that said best of luck with the project. Remember that accurate firearms have existed longer than modern machinery so we are talking about degrees of accuracy here, which depending on your goal may or may not be important. I have seen an early rifling machine at the NRA National Firearms Museum and the frame was made mostly of wood, but I am sure it helped produce arms that were accurate for their time. We need tradesmen and inventors like you to continually push the development envelope and generate ideas and inventions that advance the firearms industry.
Thanks