The pistol you are looking for is medium to large frame semi auto with one trigger pull and a caliber you can afford to practice with. If you have your heart set on one particular agency then focus on what they carry. Generally speaking your looking at a Glock or M&P, maybe a Sig. You could actually buy a .22lr and become a marksman and that experience would follow you to whatever gun and caliber you select. Purchase something relatively cheap, say a Glock or M&P 9mm or 40 cal, and then start going to schools you can afford. When you go to different trainers listen to them and keep your mind open, (one will eventually contradict another.) Marksmanship is something you learn and when you become proficient it will follow you to whatever your issued. Good luck.
Just a side note. Take some time and learn to shoot. Your ability to shoot will not help you earn a job, but it will help you after the fact. The current crop of recruits is lacking in shooting skills and sometimes they lose their job because of it.