This will sound like a trite answer but it's not: the best bike is the one you'll ride. It's the same advice I give to people who ask me what the best exercise program for weight loss or fitness or building strength. Running may burn more calories than walking, but if you can't or won't run then walking is the better exercise for you. The body is amazingly adaptable, and absolutely loves REGULAR exercise; you'll probably be shocked at how hard it is the first couple rides, then doubly so by how quickly you gain strength and stamina and lose weight once you get past that initial hump. Given your conditioning level you need to be thinking about comfort above all else, because that will keep you on your bike. Also, you're planning on losing 1/3 to 1/2 of your body weight before the Iowa tour, so anything appropriate now is likely to be completely inappropriate 18 months from now.
That said a true road bike may not be the best for you yet. You say that you're almost 300 lbs and 10 years of no exercise...that strongly suggests that the strength and flexibility in your back won't be up to par for even a comfort-style road bike. Decent mountain bikes can be had for not a lot of money. I have a $70 MTB from Academy that, actually, has served me quite well. Similar bikes can be found on CL for $25 or so. I've taken it on some pretty long rides, usually with a bike trailer and 2 kids in tow, and it rides fine. 18 speeds and index shifters won't be mistaken for quality road components but give me a lot of gear range, including a very low bottom gear for hauling that trailer up hills. The same gearing could serve you well going into headwinds. Start with the seat low and handlebars high, and as you gain flexibility and stamina you can gradually reverse these position to assume a more aerodynamic position. New or used, you won't have a lot of money in it, and can maybe save some cash for a nice new bike for the tour.