Here in AZ, I think MDF is $18 for a 4x8 sheet. I would say drywall screws would be the best but you can use anything. I just have personally vendettas against deck screws and wood screws(don't ask why). Order of construction is a personal preference like everything else in this world. I personally like to make a right angle with the back and bottom of the enclosure then do the sides and finally the front and top. For a box holding two 15s, a good set of pipe clamps should work; they are only limited by the lengths of the pipes. If you mean how exactly you do it, it's basically try as hard as you can to get a 90 degree angle. If it is a lil off, the mdf will be able to flex enough to conform to the (hopefully correct) measurements that were made prior. One tip: USE GLUE, LIQUID NAILS, ANYTHING TO HOLD THE BOX TOGETHER. The adhesive is what holds the box together for the most part, not the screws. Although I am sure you can try, I would never use only screws.
Finally, 3/4 MDF should be fine as long as you brace it correctly. Also, you may want to double up the MDF on the front where the subs will actually be resting. The movement puts enormus stress on the panel and it should be have horizontal MDF bracing as well if you intend to use only a common chamber(which I don't recommend). Sub boxes aren't hard to build unless you screw up the measurements or cut corners. Check all the measurements three times and don't think that saving a few bucks now is gonna help you in the long run. Other than that, these things are easy to make if you have a basic knowledge of woodworking.
Igitur qui desiderat pacem, praeparet bellum -- Vegetius
"I told her about my conversation three years ago with the political leader of Islamic Jihad in Gaza. "What's the difference between suicide, which the Koran condemns, and martyrdom?" I asked. "Suicide," he replied, "is done out of despair. But remember: most of our martyrs today were very successful in their earthly lives." In short, there was a future to live for--and they detonated it anyway."