The question is really hard to answer, because of stem cell controversy wherepeople of religion object against using human embryos for purpose of science.
Even though you left out the thinking about end results of everyone being able to play around with live organisms, the real spread will be built around of "what possibilities does this bring us"
For instance, while it holds true that you are able to buy computer and write your first Hello World program, in case of "lab science" it is still sufficient enough to let you do little lab play with discovering flower cells and if you feel like want to know more, there is specialised school to learn you that.
Also, computer in every household appears because it solves more than one problem of "general household" (while "playing games" might be one of them).
Long story short, even if the general public is supporting strongly the DNA tinkering, I still believe that device to play around with DNA will be part rather of "high school lab" than common household. (So, it will never reach common household).
To guess the time, I think plausible horisont to think of is 20 to 50 years.
But keep in mind, that no matter how cool the device or technology may sound on the paper, always the general public may be against it.