If you already have the basic completed (non-wordpress) HTML/CSS/JS in hand, how would you bring that design into Wordpress? Would you write your own theme from scratch or use an existing theme and apply your new design to it? If you would use an existing theme to start, which one would you use?
I like to use my own developed wordprss themes for my projects. Because free or premium themes have limitations or have huge functionality that I may don't need. Recently I made a wordpress theme for providing freebies to my users. I wanted some custom functionality into this theme which are I didn't found in any free or premium themes. But for my clients site I developed themes according to my clients requirements. If my clients needs to customize premium theme or want to use any free theme with some customization, I do that for him/her.
It's super easy to take a statically coded website to a WordPress powered theme. Just copy the post loop from the default theme, and insert the wordpress template tags you need. http://codex.wordpress.org/Template_Tags There's a lot more to it if you want it done "properly," but the above should work fine^ Then for different features/functions you need to enable/use a quick google search will turn up a solution.
Yeah you can do it, biggest branded blogs which are using wordpress platform they are using their own templates, they build it from scratch onwards. If you have good knowledge on coding part, you can try it.
I always use my own developed WP themes for my own sites or client projects.however i use "_s", "Bones" Frameworks/Starter Themes for basic code structure.
I use some existing themes if project is required to be finished ASAP. If not, then I do my own theme.
For me, I would take an existing theme and modify it. But if you're comfortable with coding, you could certainly use what you have to build your own theme. It's up to you, really.
If you developped the first site and you are skilled in wordpress theming, you probably better start from scratch. Otherwise you better start from a premium theme and start filling it with the content of the old site. I don't really believe in adapting existing free or premium themes... it takes a lot of time to fully understand what/why the original developer did...