Martin,
There are many ways to skin this cat so let me start by saying that this was my approach, it works for me, your mileage may vary.
First I went and secured a domain name, basically that is your addess on the web (i.e. www.martin.com). You can use Network Solutions to secure the name you would like to use, of course if it available.
Second step is hosting of the domain, sure you can use your comcast account but in my experience it is better to use an account that is not associated with my home internet access. That way if you move or get rid of cable for satellite or whatever, you do not impact the hosting of your site.
There are many hosting companies out there, for a site like you descirbed you will need the minimum of services. Again for simplicity's sake, when you register your domain with Network Solutions you could also hire them as hosts. Later if you are not happy with the service and you have more experience and a better idea of what your needs are you can shop around the many different hosting companies available.
SO now that you have your own space on the information superhighway its time to populate it. First your will need an authoring program like Microsoft's Frontpage or Macromedia's DreamWeaver. There are many on the market, these are two of the bigger names, I personally use Dreamweaver. You can be as simple or complex as you like with the editor, most of these programs allow you to simply drag-n-drop your pictures onto a page, wrap text around them and create links pretty easily, almost like using powerpoint. They also help you manage the many pages that will make up your site and will even upload them to your web space. I suggest pick one editor and buy a beginners reference book for that program.
The last bit I want to mention is about the galleries. My site and actually I am seeing many more sites now using the SimpleViewer 1.7 flash gallery. Its quickly and easily creates a very elegant presentation for your images that is quite customizable. The other program you will need to help you prepare and organize your images for simpleviewer is Porta. These two pieces of software are available for free on the web.
This is a lot to consider and the learning curve can be steep given your experience but it is fun and a great way to share your images and trip reports with others. If, I should say when, you have more questions feel free to call.
James