Roundup (Glyphosate) is a great product but will only kill what's green and has essentially no residual. It is a very safe product. Be careful you don't walk where you just sprayed then walk across your lawn. You can buy it cheap at a farm dealer or coop and it is not restricted use. You can buy a clone product for probably about 15 bucks a gallon. A 2 1/2 gallon jug will last for a long time. If you buy the dilute crap they sell at the garden center you will pay many times that.
Paraquat/Diquat (brand names Gramaxone, Gramaxone Max, among others) is a great product but is restricted use and is a little dangerous to handle and apply. Again, there is no residual activity with this product. If you want to see things instantly hosed you can't beat it.
Piclorum is the active ingredient in products such as Tordon 22k. It is restricted use but I believe a version of it is available commercially as Tordon RTU (ready to use). This is a dilute overpriced product. Tordon, if you can obtain it, has good residual activity but is effective mostly on broadleaf weeds and woody plants.
All of the above products photodegrade and biodegrade and are environmentally sound. I would personally avoid home brew soil sterilants (diesel fuel for instance). Because you eventually might want to grow something there or you might wind up as a superfund site and be asked to ship that parcel of property away to a toxic waste site in dump trucks which can get spendy.
I would personally go with Glyphosate and just plan on applying it a few times through the season.
