Water taxi to Venice Hotel Danieli from Santa Lucia train station

how many is "we"?

Why not just take a vaporetto?
If you are in Venice for any length of time you should get a vaporetto pass for length of stay

The No 1 vaporetto will drop you at the "Danieli" dock in front of the hotel. 7.50 EUR per person unless you buy a multiday pass.

I get that if you are staying at the Danieli you may not want to share a public vaporetto with the general public, but to estimate a correct (expensive) fare for a water taxi to the Danieli it is necessary to know how big the party is.

There are just two of us.

And we are more than happy to to take a shared transport. So (a dumb question) what is the difference between a Valparetto vs a water taxi?

The difference is roughly the difference between taking a regular taxi and a city bus.

A water taxi is like a land taxi that takes you where you want to go (if it is on the water). holds up to 10 or 12, so more like a limousine. Figure 50 EUR just to set foot in one, most trips are 75 to 125 EUR.

A vaporetto is like a city bus. Holds 100 people or so, runs a regular route on a regular schedule for the price of a ticket. There is a stop in front of Santa Lucia station. The No 1 boat goes down the length of the Grand Canal, making frequent stops along the way eventually to the San Marco/San Zaccario "F" dock (Danieli). Trip takes 40 minutes. Download the Rick Steves audio tour for guided voice over by Rick describing the sights along the way.
http://podcasts.ricksteves.com/walkingtours/GrandCanal.mp3

Cost wise, €15 for the two of you on the Vaporetto and around €110,00 for the water taxi.

As I said above if you are planning to be in Venice for any length of time you will want a length of stay Vaporetto pass.
Each single trip is 7.50€. A length of stay pass will save you money. A 48 hour pass is 30€.

Here is the vaporetto map
http://actv.avmspa.it/sites/default/files/attachments/MAP%20OF%20THE%20SERVICES%20ACTV.pdf
and info on tickets-
http://actv.avmspa.it/en/content/vaporetto

If you plan to go to Murano/Burano that is covered with a vaporetto pass, if you want to cruise the Grand Canal- that is covered, if you need transportation back to train or to the airport bus- that is covered.
Venice is very walkable but you will more than likely have a need for a vaporetto a few times a day. It's very nice to just hop on when ever you like.

You can purchase at the train station. Be sure to validate before boarding.

If you will have more than an overhead--compartment sized piece of luggage each along with a hand item, then the water taxi will likely be more comfortable for you.

Going into Venice (from the airport), we took the shared water taxi, and it was nice to have the driver stash our light luggage (I think up front), and we kept our hand tote bags right next to us. But, when we took the Vaparetto to go meet our sailboat, we took our twoRickSteves rollaboards and two large tote bags each with us on the vaparetto. We waited for a vaparetto such that we would be the first to enter (not a long wait as they leave something like every 15-20 minutes, I think I recall), and that way we went all the way to the front and stashed our luggage between us but out of the way, too.....hard to describe....even then we had to juggle the bags around or my husband picked them up at times to let other passengers by us.

Water taxi is going to be your easier choice, (with luggage) and it is a fun experience, too. The Danieli is lovely hotel, so do it right and just take the water taxi. But, later, once you are settled in, definitely take the main loop Rick recommends in his guidebook on the vaparetto....again waiting to get front seats ahead of the wheelhouse (and not all vaparettos have those seats...just depends on the seating confirguration, but easy to wait for the next one that likely will.....it will make more sense once you see the varpettoes).

Enjoy your trip!

The number 1 is usually every 12 minutes, all day.

Shall we arrange a taxi from our hotel or are there plenty of water taxi's waiting to whisk us to the hotel?

If you haven't come to this conclusion already from the previous posts, all taxis in Venice are water taxis. Same as all buses are Vaporetto. There are no road vehicles in Venice, it is travel by water or walk.

A picture may help: Click here for a photo of Venezia Santa Lucia station. The ugly flat roofed building on the right is the station.
The two floating pontoons with a yellow strip are a Vaporetto stop, with a Vaporetto just pulling up to stop.
The two small white and brown boats tied up further along are water taxis.
The boat in the bottom left hand corner is doing deliveries.

To add a little more detail to the photo in Chris F's post just above, the orange boat in the lower left making deliveries is a TNT boat. TNT is much like DHL or UPS, a courier company. The boat (with the life rafts on the roof) between the TNT boat and the big vaporetto is a smaller vaporetto used to go to the outer islands and around the larger island. It doesn't go the length of the Grand Canal, only the top bit. It is passing the larger one to go to a pontoon a little further along or just behind.