It may not be your starter clicking. It might be the starter relay, which is in one of the black enclosures on the drivers (USA) side of the engine compartment.
It's not hard to replace the starter contacts, but getting the starter off and on the car is quite a job. There are posts on the web about how to do it.
I got starter contacts for only a few dollars from the local Toyota dealer. They didn't quite fit and I had to drill out the hole in them to be larger.
I've found corrosion in aftermarket starters to be a problem. These are photos of the magnetic switch from a less than 1 year old aftermarket starter, which had a bad gasket around the cover of the switch. I took it off my 1990 Corolla 4AFE:
http://i716.photobucket.com/albums/w...agSwitch01.jpg
http://i716.photobucket.com/albums/w...agSwitch02.jpg
http://i716.photobucket.com/albums/w...agSwitch03.jpg
http://i716.photobucket.com/albums/w...agSwitch04.jpg
Another exasperating problem I had with an aftermarket starter was that it as assembled so one of wires brushed against the piston of the switch and occasionally jamme it. That took forever to diagnose!
In OEM starters, I haven't found much corrosion but the contacts do get worn down to be wafer thin and stop working.