I run a marketing company in Atlanta, GA, USA. SEO is one of our "sweet spots". We've gotten to page one of Google in as fast as 15 minutes using only ethical "white hat" tactics and strategies.
It's good that you're not using flash. I see you used Wix, though, and frankly I haven't seen much SEO value from their sites - hopefully they've changed for the better since last time I looked. But since you've already got it up and running, and if you don't have the budget for a better site for SEO purposes, there are few things that can help.
1) Keyword research: Think like a customer - what would you be searching for if you were looking for custom cabinets? What terms would you be looking for if you were ready to buy, as opposed to terms you'd use if you were just browsing or researching? You mentioned "cabinet maker" and "furniture maker" - what about "Custom kitchen cabinets" and "custom bathroom cabinets"?
2) Change your background. The photo looks cool, but some of the text is hard to read with that image as a background. Why not showcase some of your work?
3) Add more text to your site - more specific text descriptions to accompany photos of your work, tell stories about the products - rich, detailed stories that include the "how" and "why" to what you do, not just the "what"
4) Add some more pages - aside from a main page and a couple of others (contact, etc.), each page should have a specific focus.
5) Get social: Google is really taking social media seriously, and they want to rank sites that people like and share. SEO is no longer all about keywords and links - the social aspect and the local aspect are more important than ever.
6) Google loves video - and they don't have to be slick, Hollywood-style productions. YouTube and reality TV have dramatically lowered the standards for what's expected with a video. Film some short videos of you in action, talking about your focus on quality, attention to detail, and other benefits. Then upload those to YouTube and embed them on your site.
7) Blog - Google loves fresh, unique content. You could even do a video blog, and add a summary or transcription on what the video is about for your blog (and for your video description in YouTube).
Grab as much "Internet real estate" as you can - e.g. build out a Facebook fan page, a Google+ business page, a LinkedIn personal and company profile, and look for local directories to build profiles (Yelp, citysearch, yp.com, and so on) and make those as complete as possible. Many of these will get found on their own, and will also allow links back to your website. Both are helpful.
There's a LOT more to it than this, but this should really help you get things moving in the right direction.