Costs for materials vary wildly from one place to another, as well as depending on the size you want, so I'll mostly give you options for construction and you can check on local availability and costs according to your personal requirements.
Whatever you're going to be using, you'll need a flat base. A concrete slab would work, but so would a well crafted wooden platform raised on pier blocks. The most important part is how you make your sub-floor springy before putting in the tatami. Tatami is great, but with the high impacts certain throws can generate, extra spring is never bad.
Also, it's usually cheaper to design your sub-floor with extra spring and use cheaper tatami mats than it would be to use high-end tatami mats by themselves. Of course, if your budget allows, spring floor + high end tatami is the best option. Either way, there are two main options to go with for the springy sub-floor.
Recycled tires
Basically, you find as many tires of the same width as possible and spread them evenly on your training area. Then you put a layer of plywood, which you then cover with thick puzzle mats (the really thick ones made for martial arts, not the thin ones for kiddy play).
Here's an example of such a construction.
High density foam blocks
A more "standard" approach would be to use blocks of high density foam instead of tires. They are easy to manipulate and work with, and are probably more uniform in nature than a bunch of random tires. However, they likely can't be sourced for free. Most Judo and BJJ gyms will use something like that, however.
Here's an example of such a construction.
Finishing touches
As for the tatami mats themselves, if you get a decent subfloor going on, you can probably use generic martial arts foam puzzle mats such as those you would find in most karate places. The thicker ones (like, 2 inches thick) are great, and still cost much less than an actual tatami would cost (like 25% of the price, really).
I've seen some people use gymnastic mats to great effect, but most dojos will use specialized 2in thick puzzle mats (or 2 layers of 1in thick ones, sometimes). Combined with the spring floor, you should be safe enough for judo, and definitely overprotected for karate.