DocMike is right, this is the route I took too. At this time, there is such a shortage of qualified applicants, I think the playing field is definately tilted in favor of the eager and qualified applicant. Back in the 80's and 90's it was different.
Most academies will allow "non-affiliate" cadets into their regular academy. I went through the "extended format" academy which was 11 months on nights and weekends. It allows you to hold down a job while getting in your courses. It is a bit more laid back, but you are not allowed many absences, so it is a major commitment. It is mostly non-affiliates and those seeking to become reserves. Anyone sponsored at the extended academy is undoubtedly a sponsored reserve.
Being a non-affiliate at the regular academy is a major nut to crack. This means you pay your own freight. You will need to have sufficent savings or income to survive and thrive for 6 months while going to school 40 hours+ per week. Plus about $3000+ for uniforms, equipment, books, tuition, ammo and a duty pistol.
We could start a whole thread on what gun to purchase. My suggestion is to get a duty-sized 9mm. You can't go wrong with a quality, used H&K, Sig-Sauer or Baretta. Glock and Ruger have their proponents, but they also have their detractors. I am a big fan of Ruger products, but I am in the minority here in CA. I don't like Glocks and I know many that feel the same way about them for many reasons. Glock is one brand people either love or hate.
Anyhow, you don't want to have any of your Range Officers looking down their noses at your pistol choice, that is why I recommend H&K, Sig or Baretta. I suggest 9mm because it has low recoil and inexpensive ammo. If you are footing the bill, you want to get the most for your money. You will have better scores with a 9mm and you can shoot more for less. The last thing you want to do is show up with a .45 Desert Eagle, a FireStar, a Bersa... or anything with duct tape or electrical tape on the grip!
Many, many departments come to the academy and pick through the non-affiliates. Those that are excelling will get snatched up earlier in the course, you will see most all of them get picked up by graduation day.
Many departments are tending to lean toward more mature guys... in their late 30's and early 40's. This does not mean the younger guys don't have a chance. It all boils down to your background, integrity and life experience. Many departments will shy away from a 21-year-old that has never done anything except live at home with mom and dad and go to school the past 16 years. This is where the older guys and those with military experience get the huge edge. The departments call it "life experience" and there is no substitute for it.
If you are thinking about a career in law enforcement, whether you can go through the academy or not, now is the time to move on it, before the war ends and all of the guys come back from Iraq and Afgan. The need and supply are out of sync and you could use this to your advantage during this brief window of opportunity.