Hey Mike -
Welcome to the discussion. Forums like this are a good source of info, particularly when it comes to current conditions and such. But I'd recommend you start with a book. This one is fairly standard, its pretty good:
Yosemite National Park: A Complete Hikers Guide [Paperback]
Jeffrey P. Schaffer
http://www.amazon.com/Yosemite-National ... 0899973833He covers the trail you sketched, with details regarding campsites, water sources, trail difficulties, scenic points, side trips, history, geology, flora and fauna, etc. It will give you the basics and ideas for other areas of the park.
Last year we had a surplus of snow; in June quite a bit of your path was covered but not impassable. Hiking out of the valley was the only option at that point.
This year we are running at a deficit. That could change if we get a monster dump in the next couple of months, but if the Tioga Road is open mid-June and conditions permit, you may wish to start from one of its trailheads. Less effort, and way less crowded.
Have a great trip.