I have been wondering about how I could customize a Wordpress theme to look like that of my site, which is basically made of simple html and css. Alternatively, do you think there is a customizable simpler blogging solution that can be used for the same purpose?
Get the style.css file from the default theme (at /wp-content/themes/twentyten/style.css).
Open that file, you will see it is very well structured and commented. With just a few copy/paste from your current site's css to this file you will start to see the changes.
If after playing with the CSS you feel the need to change some html elements, start with the index.php file under the twentyten folder. That will change your homepage among other pages. When you have that done, you could need to do similar modifications to page.php, archive.php and single.php. Also, header.php holds the top part of the html body, of course shared by all the pages, same as footer.php and sidebar.php.
When you are done, change the name of the theme: you need to change the folder name (twentyten > mytheme) and the first lines on style.css (Theme Name). You should probably leave the Author part in its place of course. If you skip this step your customizations could be lost with the next upgrade of your wordpress install if done via wp-admin. Once done you will need to activate your customized template in wp-admin.
Try the Codex. I really love these "how can I do this" questions, please do some research.
You are faced with creating a custom theme (wordpress runs themes to visually show a different site). These themes can be downloaded from Wordpress (Extend section).
I would suggest studying the Codex here:
then follow that up by going through the default theme located somewhere in like:
/wp-content/themes/default (or any theme folder)
The themes are simple in structure, but can be turned into complex structures if need be. The codex is your BIBLE, search it if you get stuck.
My advice is using wordpress instead of other solution, as wp is the most widely used solution. you can easily find massive support articles and resources about how to customise a theme.
Or another way is to find a freelancer customising one for you. It shouldnt be very expensive.