My suggestion is to look for a bike you can use for transportation as well as exercise.
I don't know where you live but if you can use a bike for regular transportation to your job, school and friends get something with or you can put a rack for carrying stuff, fenders to keep the mud off your back and that has as simple a gearing set up as the local terrain will allow.
I bought a hybrid for a town bike and for some light off paved road (fire trails, levee tops, etc.) years ago and it has served me well. I mostly ride a road bike and when I was your age that's what I used. But it had eyelets for fenders and racks and I used them. A lot of "road" bikes today don't have those eyelets and the rear wheel is positioned too close to the seat tube for fenders.
Drop bars are better IMHO than flat bars because you get the tops like with flat bars plus the hoods and the drops. More hand positions help reduce numbing. You can get a hi rise stem to give you a more upright riding stance and flip it over as you lose weight and become more comfortable riding lower.
Good luck and let us know what's happening...