Gynecomastia surgery has really evolved over the years to the point where there is even a sort of "hierarchy" among plastic surgeons. Some have established themselves as the "go to" guys for these procedurs while other surgeons perform maybe 2-3 cases a year.
I had the surgery done last year. What led me to choose my surgeon wasn't price but was rather his track record and experience. He performed hundreds of cases a year and had before and after pictures to show the results he had achieved. Of course, nothing can be guaranteed but I felt that I was in good hands and am happy with the result.
If you go to a general surgeon I'd first ask him how exactly he plans to perform the surgery. This is much, much different and more delicate than a simple mastectomy. My other concerns would be that a general surgeon would not have much experience performing this type of surgery so your results may be suboptimal when compared with what you could acheive with an experienced plastic surgeon who has 100's of cases.
This isn't to say you're making the wrong decision. Do your research. I'd be happy to answer any specific questions you may have. Good luck with everything.