AMW
You ask some very good but very hard questions. This is just what I do and I can't guarantee this is best or only way of doing it. Hope this answers your questions.
Barry
What type of caulk do I get?
I use - Dap Kwik Seal Kitchen & Bath Adhesive Caulk
Do I have to remove all the caulk that is already there?
This is a hard call. Unless you remove all the caulk in the shower at some point you will have to bond to existing caulk. Is it better to bond in a corner or in the middle of a long run? Personally I don't think it matters. In either case you have two points of bonding and therefore two points of possible failure. My choice would be based upon how things look when finished. If I think it is going to look like a patch job I would remove the caulk back to the side walls of the shower.
Always remove any lose caulk.
and if so how?
Removing caulk is just a matter of pulling, pushing, scrapping, cutting whatever it takes to get the caulk off. I find pieces of plastic with sharp edges work best for me. I have also heard of some solvents that will dissolve caulk. My concerns with using solvent are bonding issues because of solvent residue and harmfulness to the shower wall itself. I have always just scraped and then wiped with alcohol.
When I start to remove caulk I cover any drain with masking tape to keep the small pieces out. A shop VAC with a brush attachment works great to get all the little pieces.
or do I just make sure it's clean and dry and add caulk right over the existing caulk?
Always remove any lose caulk
if so, is there anything I need to do to prep the surface for the new caulk (besides cleaning and drying)?
I usually clear the area with alcohol and let dry. Just make sure there is no lose dirt, dust, old caulk, oils or soap etc.
Here are a couple of tips I have pick up over the years.
Apply masking tape on each side of the caulk line you want to make.
After you apply the caulk wet you finger in warm water and use it to smooth the caulk line.
Let the caulk set up a little before removing the masking tape. Do not allow the caulk to cure before removing the tape.
Practice a little on something you can throw out.