There is actually no problem, everything is working as expected.
The automatic prompt that MiKTeX throws up when a missing package is detected silently downloads and installs packages without producing much diagnostic information. Most packages download and install in a matter of seconds, and this works fine.
cbgreeks, which is necessary for the functioning of textgreek, is almost 70 MB large. Even if you have a fast connection, your nearest CTAN repository server may not be able to provide a very fast upload rate for you. Therefore, downloading this package takes a long time. And the TeX compiler must wait until the download finishes.
In theory you could just sit there and wait for an indeterminate amount of time, and eventually the download will finish and your compiled PDF will probably appear. For such a large package, however, it's better to use a more informative interface: Go to Start Menu -> MiKTeX -> Maintenance -> Package manager. In the Name field in the top right, type the name of your package (eg. cbgreek). The list should be filtered to show the package you want. Right click the package and select Install.
You will now be able to watch the progress of the download and installation. If the problem is indeed the package size, you will also be able to observe more clearly just how long the package takes to install.
After installation of your large package(s) is complete, TeXstudio should be able to compile normally.
The error message "Fatal format file error; I'm stymied" means that TeX binary is trying to load latex.fmt (or pdflatex.fmt) but the version of this TeX binary differs from another TeX binary which created such latex.fmt. There could be two reasons: you have installed two TeX binaries (in different versions) or you have somewhere in your computer the old latex.fmt from previous TeX installation.
The pdflatex.exe must be implemented as one what runs TeX binary (most probably pdftex.exe) and sets the message to this binary: "hey, load pdflatex.fmt". And this loading is broken as described above. I don't know how exactly it is implemented in MikTeX, sorry. I never used MS Windows.
New TeX distributions has more TeX binaries: "tex", "pdftex", "luatex" and "xetex". If one of them creates file.fmt and another of them reads such file.fmt then the error message mentioned above occurs too. This is reason why TeX distributions save the generated file.fmt to directories specific for used TeX binary and they have implemented a searching system over such directory trees.
Best Answer
Short answer:
dvipdfmx.Longer answer:
dvipdfmxis an extension ofdvipdfm, enabling access to more PDF-specific features. As such, it implements a superset of the features ofdvipdfm, and is more powerful.dvipdftis a tool to usedvipdfmto make thumbnails (according totexdoc dvipdft). As such, it's not what you want at all!