I had a brand new coil go bad on me in a few months, and I hardly ever started the car in that period. Also, check the voltage at your starter solenoid. My brand new one went bad a few weeks ago and it can do some freaky things. They are also pretty cheap, and a (cheaper) manual type will work completely fine with your automatic.
If you get a chance to look at your starter, they are fairly simple to remove and take apart. WAY easier than a carburetor. Just remove two bolts and pull it out, then you pull two screws to open the case. Inspect the drive gear and make sure it moves smoothly, and give it some grease while you're in there. Also, take a can of electric cleaner to remove any gunk that's built up, and make sure the brushes aren't totally worn away. Then throw it all back together and bolt it back in
The brushes are the four copper pieces on the outside of the middle circle (armature). They shouldn't be much more worn down than this.
This is the armature, with the drive gear on the left.