I think this has been explained already, but be a police officer doesn't allow you to purchase anything that a normal citizen cannot purchase, unless your state has some restrictions that most other states don't have. It certainly won't allow you to purchase anything NFA. Your agency may well purchase a machine gun, SBR or SBS and assign it to you, but it belongs to them, not you. They can take it away at will, and when you quit, it goes back to their armory. No, there are no exceptions. The ATF has no sense of humor about such things.
You may be eligible for carry without a permit, depending on the specifics of the law in your state. I'm sure your department will train you about what you can and can't do in that regard. If they don't have a policy about you carrying concealed and it is never mentioned in training, I am 99.9999999999999999999999999% certain that you can't. So don't. Period.
You probably will be eligible for department or LE discounts on firearms and associated gear, but that will be up to the individual retailer. A word of advice? Don't be afraid to ask for discounts in areas where you should get a discount for your work. Lawn care suppliers offer discounts on seed and fertilizer to lawn care businesses. Home Depot offers discounts to contractors. This is no different. HOWEVER, don't be "that guy" asking for discounts at restaurants and other businesses. If you're offered a discount, be thankful and appreciative, but don't go trolling for free crap. If you go to a restaurant where cops "always" get a discount, have enough money to cover the full bill, and have some grace if you don't get "your" discount. Pay your bill, press on. Everyone else in the restaurant is paying the full tab, don't disgrace yourself, your agency, and the rest of us by asking for something for nothing. The local coffee shop never charges me for my nightly cup o' coffee, but you know? I always have a fiver in the back of my notepad wallet in case I am charged, and if I have spare cash I make sure I drop something in the tip jar...the baristas are working, too.
Be safe and do the right thing.
Mike