I've never really used Starting Strength. Not sure how it would defer what I usually do. I tend to try and lift weights that let me do 6-8 reps. Once I can do 3 sets of 10 reps, I up the weight by 5-10 lbs. So far I'm increasing weights after 3 lift days of the same weight.
You are free to do whichever program you want, of course, but there's a reason why so many of us recommend Starting Strength: because it works better than any other program for novices. It's basically fool proof and algorithm-like in its simplicity and efficiency.
There's really no better way to get stronger in a short period of time.