Cincy Boy's scenario will get you a very good grow in a minimum amount of time. It is the most common scenario, almost everyone grows that way. And why not? It works, plain and simple.
YOu can be cheap, if you need to. My main focus in starting my grow and keeping the costs down were to have everything fly under the radar as much as possible. Cincy's example will have an appearance of running another computer, all day long. Here's what I did:
I purchased 3 "energy-saver" fluoro bulbs, 3 plug-in work lights ( the kind you use to work on your car, just take off the metal part that hangs), a power bar, a bag of soil, 2 planters, seeds (10 for 70$) and a watering can. I paid cash for everything, as to not leave a paper trail. The 3 bulbs equate to leaving the bathroom light on all the time ( no spike in the electricity bill, that's the key to no detection). The grow is a little slower, but suffices my needs and goes undetected (by cops and my wallet).
It's all about determining what you need and finding your niche.