Emily Lakdawalla at Planetary.org has done a nice simulation of what to expect when. We'll get some good images of the Pluto and Charon, at up to 12.7 kilometers per pixel resolution returned by Sunday 12th
By comparision, this image of Ceres is 14 km / pixel.
So - not great resolution but enough to begin to see features. E.g. we'll surely see the ice caps if Pluto has them. Pluto may be quite dramatic already at this distance because it has such variation in colour and Albedo, far more than e.g. Mars or or Jupiter.
Then on Monday 13th July we get an image of Charon at 7.2 km per pixel and Pluto at 3.9 km / pixel on the 13th July - these are the "fail safe" images which it returns before the encounter just in case it hits something during the encounter itself (though the chance of that is now thought to be tiny).
Again compare with Ceres, this is 2.5 km / pixel
So we get one image of Pluto at approaching this level of resolution before the flyby. This a fail-safe to make sure we have at least one decent image of Pluto no matter what happens.
It doesn't return anything during the flyby itself. The reason is because its radio antenna which it uses to send the images back is fixed in position (to save on cost of the spacecraft) so it has to turn the entire spacecraft to beam images back to Earth and can't take photographs at the same time that it returns them.
So we don't hear anything from it at all for 24 hours, it works entirely autonomously taking all the photos for the flyby, until we hear a "beep" from it on the night of Tuesday the 14th to say that it got through safely. At which point everyone can breath a sigh of relief :).
Then the highest priority images are returned after the encounter, by Thursday 16th and then another batch by Monday July 30th. These are close up photographs at a fraction of a kilometer per pixel.
After that they have a gap of nearly two months downloading instruments with low data volumes and just house keeping data for everything else, but no images until it is up to date with everything - by September 14th. And after that it resumes downloading images, this time lossily compressed, will download everything it took, but with image artefacts, so we can see what it's got. That takes it to around November 16th. After that it downloads everything high resolution.
There, it will be possible for the team to choose to prioritize any especially important images to be downloaded first.
It will take over a year to download everything, just because the download rate is so slow from such a distance and with a not that powerful antenna.
Here is her simulation, using voyager images of Jupiter and Saturn's moons to stand in for Pluto and Charon. This mosaic covers all the photographs that will be returned by the end of July.
As for the next batch of somewhat higher resolution photos, we should get those starting at the end of May. Since we already found out that Pluto very probably has an ice cap in the photos already maybe these will give us more details. With its large variations in brightness and darkness then we can hope to begin to see features at an early stage.
Most of the photographs taken now are binned, where the camera pixels are grouped together in 4 by 4 bins to make a single pixel - that's because in that mode then they can pick up faint moons.
Our first reasonably high resolution image of Pluto and Charon according to that timeline is 28th May when we get a non binned photograph with a resolution of Pluto, Charon, Nix & Hydra with 281 km / pixel. Similar to the 1st June non binned image above. But since we already see an ice cap with the binned photographs, then surely we will see more details in that image than we see in Io which just seems featureless from a similar distance.