I agree with firegoat. There are some very specific situations where doing length and girth together will be problematic though none of them apply to the manual exercises found in the newbie routine.
However, just for your information, those situations are:
1) if you are doing very advanced length or girth work, recovery could be an issue and piling the other kinds of exercises on top can push you over the edge. For instance, if you are seriously clamping then you probably need a good deal of time just to recover from the clamping and adding serious length work to the mix, aside from basic manual stretching, will make it even harder to recover.
2) because stress is a function of force and cross sectional area, very large girths will require greater forces to achieve similar results. But most people will not all the sudden wake up with a 7” girth after doing the newbie routine for a couple months. :)
3) if you are doing PE that requires a large time commitment, such as hanging, practical considerations will get in the way of adding the other form of exercise. Things like life and responsibilities.
You are new here, and I’m sure you don’t fall into one of the above categories (yet), so really doing both together would be fine.
As to the best way to target base girth, I would say that is probably hanging. I hang primarily, and unlike many here, I don’t believe hanging is dangerous for a newcomer if they take the time to learn everything they can and are smart about it. Since I started hanging, my base girth has increased about .5” while my mid shaft girth has not increased at all. Hanging is definitely not right for everyone though and it requires a modest investment of money in some cases, so do some research before you make that decision.
However, for now I think firegoat is right, and unless improving base girth is your ONLY goal, I would focus on general PE first before specifically trying to target base girth. And baseball bat shapes are kind of cool in my opinion. :)