It is normal for the headlights on a car to dim slightly when the ignition is engaged due to the large current draw of the starter. If the dim is more than normal, there is a problem.
My 98 corolla also had a starter problem where it was clicking and I called an auto electric shop and they told me that most likely the solenoid contacts were bad. I bought new contacts for $10, removed my starter and installed the new contacts (the old ones were very worn), reinstalled the starter and now it works great

. I can post a picture of the worn contacts if you like.
-Chris