Caulk the vanity to the wall (IMHO). Water will drip behind, otherwise... even if just from cleaning. I have glass tile halfway up the wall behind my new vanity, but I still caulked the edge of the vanity and sinks to the tile. And darn glad I did, since I totally splashed water all over it washing my face yesterday. I would have been freaking about water running behind and possibly swelling the plywood of the vanity bottom and sides. I admit I was nervous to caulk. I loved how it all looked just sitting together, with the slight shadow line between the porcelain, wood, and glass elements. But I taped REALLY carefully, right on the edge of everything, so the caulk beads are very small. They don't detract too much at all... and after that big splash yesterday and I can definitively say we made the right decision to caulk.

Hey Tracey Strangely enough I'm a Sales Mgr for a sealant company (caulk opens me up for too many jokes, ha). First question, Are you painting over the caulk? Second, If you are using it near water I would not go with a Latex, because water breaks down latex and eventually you will have failure. Even if it says silconized latex, it is still a Latex and the silconized part is mainly a marketing ploy. If I were doing my bathroom I would use a product called Lexel. It is a clear(literally crystal clear) elastomeric co-polymer, so no ugly caulk line but all the same benefits of a silicon and it's paintable if you ever need to paint it. Also, it will bond to marble with out etching. My second choice would be a Neutral Cure Silicon, which is important because other varieties of Silicon are cured with acids which hurt Marbles and Granites.

Caulking the gap between tile and the toekick isn't bad, but usually not necessary. Most times a piece is installed over the toekick to match the vanity's finish that hides that gap. That said, you usually don't have a half inch gap. To me, that would be unacceptable. But I get the feeling the installer may not have checked his coursing, and that's the edge of a full tile. I'd like to think that he didn't deliberately put a joint that big there cutting the tile into the toekick!

The first thing is to determine where the home’s shut off valves are. That’s inside the dwelling, and outside at the street or meter. If there are shut offs under those sinks, they likely are frozen open and will self destruct when you try to use them. Next, figure out what type of plumbing supply lines that you have. CPVC? Copper? What material supplies are you going to need? Go to the store and get some stock fittings, glue, solder, etc. You'll need all of that now and for future projects. Next, Shut if the water to the home, at the main shut off, and drain the internal pipes by opening the most downstream one to drain. Cut off the shut off valve and glue or sweat a cap to them. If you haven’t sweated copper bis fire, practice that for a week or so before tackling this. Any water in the lines will make this really difficult. Leave the pipes long enough to be able to extend with new pipe or a new valve. Cut the drain waste arm going into the wall. And stuff a rag in it. Trim up all the spaghetti hanging down from the top for easier handling. Once the pipes are capped, then cut free the caulking holding the top to the walls and vanity. A long slim blade, and then a cat’s paw pry bar will be needed. Then a bigger pry bar. These things are much heavier than you think they are. You will need help to lift it up and off. Once the top is off, then find all the screws holding the vanity to the wall, and remove them. Look for screw at the bottom too, holding shims there. You and your helper tilt it forward to be sure you haven’t missed a screw. Then slide out the bottom. You likely will have some wall damage to repair. You can put it on Craigslist to sell it or donate it if you don’t damage it or the top. If you damage it, use a sawzall to cut it up into manageable chunks to dispose of. Many municipal waste companies don’t like construction debris in the household cans. If that’s the case here, you’ll have to haul it to your local dump. Some will require a dump fee. Some allow so many free trips per year. Use that opportunity to get rid of a few more things in either case. Putting in a new vanity, top, and plumbing, is more than twice as hard as demolishing the old. It’s an advanced DIY skill. You need to own multiple levels, and know how to shim things to level in all 6 directions. Then you screw it to the walls through the shims. Install the faucet to the top first, before setting. Shim the top level, and silicone to set. Then you redo all of the plumbing. I’d suggest making friends with your new neighbors and find a friend with some DIY skills that you can help with her jobs a time or two before tackling this. You will need tools. Those tools will cost as much as hiring a pro to do it for you. But you get to keep the tools to do it again! Good luck!