There are many ways to make a website. You can go with something like webs.com, you can make a site from a cms like wordpress, or joomla, or you can make a fully custom website with photoshop, html, and css. You can have it programmed from scratch, you can use ready made html, you can make it in flash, etc. It all depends on your skills, time, and budget. I am 17 and got into website design almost a year ago now, and from my experience I can tell you that website design can be VERY complex and expensive depending on what you want. I have worked with people who charge $20 per hour, and only a few hundred dollars for a simple 5 page website, and I have worked with people who charge $150 per hour, about $3,000 for a 5 page website. So it depends on who the designer/programmer is. I am now in the process of starting my own company to design websites and program for all budgets and you can probably find someone to suit your needs if you look around. If you need help, I can offer it and can help you find someone. Hope this helps.
Another inexpensive option is to host pictures of your animals on free sites, such as Flickyr. You can even post comments. It's not a genuine website per se, but it performs the most important function for free (ie. advertising your animals) and the photos are easy to link inside forums.
I was in search of a website too. My boyfriend ended up looking around for me, because I do not understand websites at all! or how to make them or anything. It gives me a huge headache. So he is designing one for me, and the website that he is making it through only charges like $5 month.
I would really like to see who the big timers use...
I use Yahoo web hosting. Which comes with an awesome page builder. Do most my graphics on photoshop. Then just add them to the site using yahoo. Yahoo web host use to be called Geocities. When it was Geocities it was free but had ads
we use justhost.com website builder. Although our site isnt as fancy as others, being a full time student I and working I dont have the time to make it super fancy, but the price is great and it is really easy to use. I have in the past used go daddy and I have to say it was horrible to use and I had alot of problems.