Ok, the new starter has been installed and the car starts beautifully. I got a Bosch part from Pepboys, which set me back about $150 + tax. This was the cheapest I could find and still seems like a lot.
Here are the steps that I followed to install the new starter:
1. Removed intake hosing along with the top of the air filter box. This allowed access to the two bolts attaching the starter to the engine. The bolts were still hard to get to since multiple wires were in the way.
2. I had to jack up the car and go underneath it to get to the starter itself and detach the electrical connections. I believe I used a 12mm wrench.
3. Then, I unscrewed the two bolts holding the starter. This has to be done topside. Used a long extension and a 14mm socket, per AsleepAltima's advice.
4. Got under the car again and removed the old starter.
5. Installation of the new one was following the reverse process.
By the way, Autozone does free starter analysis. I brought my old starter in and it failed the test. I did that before I put the new one in, just to make sure that the starter was causing the problem.
Finally, I'd like to thank AsleepAltima for his advice and I hope that this thread will be useful to someone with the same problem.