Hi Tim 
As far as getting the data from your software to web space you would want to see if the software itself has a built in function to do this, as Weather Display and other paid software does. I would really investigate utilizing the software you already have to its full capability and see what it can create and upload for you.
Now what to do with it after you get it there.
My site is PHP based which allows a number of options such as includes, allows you to pull in full html files directly into another page for formatting and layout purposes. I also use my own layout and navigation and the “iframe” tag for including some files from other directories, along with their images.
I first designed an overall look, using basic HTML, that I liked. Then once I had the basic colors, header left navigation and bottom (or footer) all set the way i wanted I split it into 4 parts, basically…
header.txt
footer.txt
nav.txt
and then a file that called each of the above elements, using PHP include statements, and then in each separate file I added content to the center of the page… This is very simplified but is the basic method I used.
Now this allows for modularity and if I want to change a link in the left navigation i can change one file and it changes for every page that uses that navigation file. This can also be done, to a bit lesser degree using SSI (server side includes) however SSI doesn’t support as much flexibility that PHP does, IMHO.
I always start any page design using Nvu, which is a Free WYSIWYG (what you see is what you get) HTML editor based on the Mozilla Composer module. http://www.nvu.com/
Then I upload a sample and tweak it on the server directly as Nvu has limitations, especially in saving PHP code. Once I have the look i want then it is really just adding content to each of the pages I am planning on. My site started with about 5 pages and has grown to about 25 main pages, four separate applications, HamWeather, Picture Gallery, GuestBook and Station Log and I still have more to add, such as tide, fire danger and soon Lightning information… (just got to figure a better navigation system, i hate drop downs) LOL
Hope this helps a bit,
Bob