Those are some fine looking pipes! Take your time and don't rush anything. There is lots of pipe restoring info on the google-net ... unfortunately most of it is either not good advice, or is just plain dangerous to your pipe. So, if you will indulge me, I would like to pass on some things I learned while restoring an old Stratford that I had picked up.
Ignore any advice to use hard or sharp tools - drill bits, knives, etc. You don't want that stuff near your precious pipe.
Ignore advice to use cleaning agents that you would not use on your best eating implements and is not "food grade". What goes on the pipe goes into you.
I scraped and rounded my bowl by patiently working it with the "scraper" on my pipe tool. It may be out of round by .05 millimeters, and that is fine. It's an old pipe, after all.
If you need to clear the shank hole or the stem, use high test vodka or similar consumable alcohol and pipe cleaners to slowly dislodge the carbon and work it loose. Trying to push the stuff out with hard tools only risks damaging surfaces. Oh, and don't soak the briar in the alcohol (you can soak the stem though).
An awesome tip for cleaning the lip of the bowl and the finished outer briar surfaces ... spit on a cloth, then rub it on the briar. This is guaranteed to remove any carbon "charring" and most any other detritus that may have accumulated on it. To finish the briar, use some carnuba wax, a Dremel buffing wheel (only on the slowest setting) or soft cloth, and apply elbow grease as required.
The vulcanite stem on mine was pretty oxidized. I used a bleach bath. Yours has a logo on the stem, so you will have to protect it with petroleum jelly or the bleach will remove it. For polishing, rather than using petroleum-based concoctions, I chose to use a product called "Bar Tenders Friend" which is a food grade cleaner that polishes as well as any purpose-sold polishing agent I have found. Lowes or somesuch should have it, and it's cheap. Mix a little water to make a paste, put some on a Dremel buff wheel or a soft cloth, and then put some elbow grease to it (only use a Dremel on the slowest setting). Carnuba wax will give it a nice shiny finish.
Finally, protecting the vulcanite will be your biggest challenge. An excellent solution I use is to keep a small cloth with a couple drops of olive oil on it. After each smoke, I give the vulcanite a quick wipe and it's good to go. So far, not a hint of oxidization.
Hope this helps!