Howdy!
Been there done that :)
When I first started out I would LOVE 800-1000 for a site but, after 20 years, I’m in a spot where I can choose NOT to work with clients with such low, unrealistic budgets.
Here’s some things to consider based on my experience:
1) It seems ALL of my low budget clients were the HIGHEST MAINTENANCE! If you do lower to their budget, please follow the advice of others above and get EVERYTHING in writing!
2) Although it’s true that I’ve roughly based my project costs by time, never forget the VALUE of a quality website. Some businesses pay hundreds PER MONTH for a yellow page ad that nobody uses…isn’t a website worth so much more?
3) If you do meet their budget, your idea of customizing an existing theme may work very well. I’ve done this with the client expectation that they choose a theme and I ONLY update logo and colors. NO custom coding!
A colleague shared something with me when I first started – “If you charge nothing, you’re worth nothing.” I immediately doubled what I typically would charge and haven’t looked back :)
Good Luck!