Your past performance will matter more or matter less depending on where you apply. Your LSAT score is key, and high score will give you much needed leverage.
When you apply you will have to write an addendum explaining why you were on academic probation, even if it was in 1996/2003. This isn't optional, as both LSAC and the individual law schools require it. Be honest and explain, but try not to make excuses. Your most recent grades and LSAT will be the main factors. Try to boost your GPA as much as possible and seriously, seriously study for the LSAT. A high LSAT score can do wonders for a lower GPA.
The law school admissions process is incredibly numbers driven. Issues like grade trend are not really primary factors if your GPA/LSAT profile is above a given school's average. Those schools will admit you on the strength of your cumulative numbers. Why? Because it raises their median numbers and makes them look better. If, however, you apply to schools where your profile is average or below average, it might become an issue. I would advise applying to schools where they want people with your LSAT score (whatever it ends up being) to make their numbers look better, you'll probably get in regardless. At more competitive schools, not so much. Those places have so many highly qualified applicants to choose from that you have less leverage.
I was in position somewhat similar to yours: I started law school in my early thirties and my GPA from 10 years past was mediocre. I focused on the LSAT, spent a couple of months preparing, took tons of practice exams, and got a great score. In my experience a high LSAT overcame an average GPA, and I received a 75% scholarship to my school of choice.
Start preparing for the LSAT now. Buy some prep materials and familiarize yourself with the test. Identify your strengths and weaknesses early, and tackle them. The other factors you mentioned (veteran, WS major) are soft factors. Your numbers will determine your choices. I don't know if you want to remainin Sacto, but a mid 160's LSAT and a mid 3's GPA would probably get you a scholarship to McGeorge.