You shouldn't have any problems getting maps from gas stations to get you going. Your budget seems fine so no problems there. For Zion I would look at stopping in Springdale, it's right on the doorstep of Zion and the free shuttle buses into the canyon run from town, Ruby's Inn at Bryce is pretty cool as well.

Good idea with the camping, although there is no guarantees that you will find camping in the NP's either, but hopefully.

Looking forward to the updates, have a great time !