I think a dog run is a great thing and every dog should have one, but it really does depend on your neighborhood how safe your dog will be in there.
If I had to do it over, all of my dogs would have a doggy door from their outdoor run to an area inside. The dog doors I currently have I use x-pens on the inside and it works great. They have a 4x4 area inside (x-pen hooked to the wall with self-tapping eylets and clips.) And a ten by 20 foot kennel outside.
Dog runs depend on where you are located. If you are located where there is considerable snow, you might consider having your gate 1' above the ground level. It would mean stepping in and out of your kennel, BUT you will not need an ice breaker and build your muscles up shoveling and pounding away the ice just to get the kennel gate open.
One of my kennels, due to its location opens in ONLY. This is a HUGE mistake in the snow belt. Sometimes it is extremely difficult to squeeze in there to break up the snow to get the gate open. The dogs pack it down somewhat, but it is difficult.
DO NOT BELIEVE YOUR CONTRACTOR ABOUT SLOPE. They are full of doo doo. What ever your contractor says, double it at least. Otherwise you will have pools of water lying in your kennel.
If money was no object, roofing the kennel would be nice. But in any case, you should put a lighter gage wire across the top of the kennel to prevent a climber from escaping. Also the dog house could be a stepping stool to the outer world if the kennel is not covered over. But I believe having a dog house is essential if the run does not have access to the house. If the run DOES have access to the house, the fencing should be on the house side as well, otherwise a chewer could chew the siding off the house.
I suggest a concrete base. It eliminates any thought of digging out. Generally it is easy to hose down and maintain. If I had to do mine over again, I might have built up the sides with concrete blocks for a few feet as well. I use 9 gage wire for the gate and the fencing.
If you are 5'7 or taller, the roofed over 6' kennel will be a pain in the winter when you forget your are walking on eight inches of snow and crack your head on the two by four running across the top of the run.
Good luck making a nice run. I think mine are good. They are fences around as well, just in case I am stupid with a latch, they will still be inside a fenced area. I will look for a picture.
Notice how I did not fence the house side and the dogs went to town on my siding:
Comfort is a biggy, notice the water bucket in the bucket holder -- with these I have NEVER come home to a dog who spilled their water and were without. Also cots to give them a place to rest off the concrete, and my dog house's floor is elevated from the ground and I have a dog shelter in there, this one has a lawn chair -- well, they do like them. (spoiled)
This one shows some of the use of tarps and the dog shelter:
Ordinary tarps can be put along the side of a kennel to provide shade, but not across the top, or it will collapse the kennel if a major rain fall happens. I use sun screens on the top of the kennels which effectively lower the temperature inside.
ETA: the last two photos are one kennel -- two different views. The dog shelter is 8' long by 4' wide, and tall enough for the dog houses to be inside, and the dogs leap on top of them and lie on them.