Buy the PCBs from Falbatech. You can decide then if you want to pay a little more to have it partially assembled for you. I'd suggest having them do the SMD components at least. While you can source these components yourself from the web for marginally cheaper, the trade-off is you will spend significantly more time soldering them and, at least in the case of SMD components, there is a skill and equipment barrier that you may not be prepared for. It's up to you to decide if the additional $15-20 is worth it or not.
The PCB is the hardest part of the build and it's where 90% of the work is done.
Your second biggest concern is the case. If you're any good at working with wood then you can make your own case by hand. That's the cheapest option, assuming scrap wood and you already have all the necessary tools. After that, acrylic and PVC are your next cheapest options. You can find both cases at Falbatech for $30-50. Every material has certain drawbacks. Remember to get a plate.
The rest is easy. Order the Teensy separately and solder it yourself. Source your switches and stabilizers (optional) from the cheapest place you can find -- mechanicalkeyboards.com has been a good source for me. Massdrop may also be an option if you're willing to wait. You can get keycaps second hand, like in the GH Classifieds, or just harvest them from a few other boards if you're desperate. You can find a Mini-USB cable just about anywhere and probably have one laying around in your house. Monoprice has TRRS cables for $2. LEDs are only a few cents each but if you don't already have some spares then you can just skip them -- that's what I did on my first Dox build.