Part of this depends on the quantity of reactions you're doing. Taking the DNA barcoding of trees example we gave, if you're doing hundreds of reactions the cost can already be quite low as crocowhile pointed out. If you're just learning or doing a few reactions, here's where a kit containing small quantities of the needed reagents and educational information can be more cost effective.
The other part has to do with the exact reagents you need. Obviously if you can use an off the shelf master mix you'll pay much less than if you need to purchase a specialized enzyme and specific reaction buffer. There are cases where that is needed, but there's also cases where people purchase reagents more expensive than what they need, simply because they just want their reaction to work, they've found one way to make it work, and they'd rather spend more time on their project rather than finding the more cost effective ways to make it work.
Here there's a lot of opportunity for software or software coupled with hardware to find the most cost effective way to do a reaction and make it work better. For example, a PCR machine networked with a UV spec and some software could quantify template DNA, present recommendations on enzymes, calculate the best reaction parameters accurately, and tell the user exactly what quantities to add of primers/enzyme/buffer/water. Many users of PCR are not necessarily experts at PCR, so there's some opportunity to help people get better results while saving time and money.
We're thinking about these larger problems, but focusing on getting an accurate and reliable PCR machine working first. Once we have that, we'll have the foundation to pursue these other areas.
The typical way of visualizing DNA is using an electrophoresis gel - most of the components are cheap/easy to obtain (agarose, electrodes, power supply, buffer), but how would you visualize your gel? Typical ethidium bromide stains are probably out of the question, given that ethidium bromide is so carcinogenic - most people probably don't have access to ethidium bromide. Maybe use a safer stain? (googling seems to point to invitrogen's SYBR Safe DNA stain as a possibility).
Then again, you could just use a UV spec to measure concentration, but how many people have a UV spec?
Looking forward to your results! In the future I think it would be nice to have open source enzyme starters (kind of like brewers/bakers yeast starter kits?) so that people could just grow+purify their own enzymes. (after the open source centrifuge that is =P )
Provided you have a PCR machine, a small centrifuge and an apparatus to run DNA gels an experiment like the one they are mentioning (finding out the kind of tree you have in the backyard) would cost you something like $50-$100 if you really know what you are doing. Much more if you are not a pro.