If you are after a very simple HTML/CSS site I can recommend a tool from the earlier days of web building, this tool is an editor which composes everything for you in markup, it saves a lot of 'grunt work'.
The tool is called: Komposer
I have found this to be extremely useful over the years.
With Google docs, you can provide a shareable link, and set that link so that anyone with it can either view, comment, or edit. Obviously, the view option is what you want. It looks like you can do this with an entire folder too.
> When I decide to publish it as a webpage publicly, it throws off the entire layout
Are you publishing stuff as a web page from Word directly? Word is ~~shit~~ not good for this kind of thing. In your case, I would get a free WYSIWYG HTML editor like KompoZer, copy your content from Word into a plain text editor like Notepad to remove all of Word's inline formatting, and then paste that into KompoZer and reformat it. That will give you an HTML page that will look like what you expect it to look like.
If that's not what you're doing you'll need to provide more detail as to the process and what exactly is going wrong for anyone to be able to help you.
Yes, most any HTML editor would allow you to create tables without the need for a graphic, and much more flexible to change as needed.
Kompozer is one that comes to mind.