I am interested in getting some objective information about the acoustics of my current set up in the hopes of making some changes for the better. I was thinking of using something like Room EQ wizard.
Room EQ Wizard is a wonderful choice, I use it myself.
First question-do I need to get the radio shack SPL meter and a tripod?
You do need a microphone, a Radio Shack SPL meter is the easiest option. A tripod is a good idea, as you need to make multiple measurements in multiple locations in the room; a few where the primary listener's ears would be and also at other listener positions (but focus on the main listeners).
Second question-I will be using a macbook and using the headphone jack to plug into my receiver so that it can transmit the tones. I think I was reading something about how using the headphone jack had too much noise. I don't have a computer with a dedicated sound card. Is there a better option?
If you don't use a good sound card a true measurement microphone and a calibration file for the sound card and the microphone the results will not be accurate. But for what you want to do, I don't think the inaccuracy will be a big problem, you will still be able to make some improvements, just keep in mind that what you see on the monitor isn't an exact reflection of what's happening in the room.
I don't remember hearing anything about a headphone jack being too noisy, I have heard that the frequency response of a headphone jack usually has low frequency roll off, so depending on where that starts it can be a problem. Also, a laptop may not handle the bit depth and sampling frequency of the signal from REW, but you can buy an external sound card, or find some software that works better with your hardware.
Third question-Assuming I do all these measurements what can I do to improve whatever weaknesses exist?
The only improvements that can be made relate to low frequency performance; you will be able to see and address issues in bass response. Mind you the only way to address the problems is to move the subwoofer, speakers or your chair (though it may not need to move far).
Now you may wish to fix more than just bass response, but it is not possible to see all acoustical issues with room measurements, nor is it possible to fix them all - especially since many (many) problems should have been (and can only be) fixed by the manufacturers engineering department.
