Improved Pursuit AI - It's rather new, but I have taken a liking to it already. In my experience, most pursuit AI enhancers have a heavy performance toll, but this one doesn't take frames away for me.
Ultimate backup (W/SAUB if using EUP) - This mod brings a whole new world of possibilities for backup, from performing felony stops to having your backup stick around until they're dismissed.
ELS - ELS allows you to have 4 stage sirens controlled by number keys 1-4, and emergency lights to be activated independently from sirens. Make sure you install vehicles that are compatible with ELS (ELS compatible packs I use: LSPD, BCSO, SAHP)! If you aren't comfortable with installing vehicles, I highly recommend DLS instead.
EUP (W/EUP Menu & EUPSR) - These mods completely overhaul uniforms, and allow you to expand beyond the default departments, even into fire and medical. Note: To select outfits, you'll need EUP menu, and you'll need SAUB or a different ultimate backup EUP configuration for your fellow cops to wear these outfits if using ultimate backup.
Better EMS - If you've called for medical before, you'll probably notice how terrible they are. Once they magically warp into the next block over, they mindlessly plow through traffic, only to perform half-assed CPR and call it a day. Better EMS incorporates medical response time, and reworks survival chances.
Deadly Weapons (Debatable) - I can't really determine whether this mod is right for you, since it really depends on your playstyle. Deadly weapons makes guns highly lethal, to a realistic, and sometimes frustrating point. I recommend giving it a try to see if you'd like it. Note: In the deadlyweapons.ini file, you can modify settings, such as disabling the gunshot activated panic button.
Basic Parking Enforcement - Basic parking enforcement is great for slower parking ticket RP. GTA tends to spawn cars in strange locations, so this is a great tool for that. I do advise changing the menu key in the INI file to something else, as it's Q by default (the key that makes you duck to cover).
These are only a few of the mods I use on a daily basis. I recommend that you install some callout packs, as LSPDFR only has 3 out of box.