Police notoriety ideas: Level 1 starts off with Stilwater\Steelport PD officers using melee weapons (baton, billy club, taser, pepper spray) and pistols.
At level 2 officers will start to use pistols and shotguns also some officers will start to wear bullet-proof vests (like in SR2). Sheriff Deputies armed with semi-auto rifles also have a chance to spawn in their own unique variants of the Five-O and Peacemaker.
At level 3 SWAT and Riot Units are called in. Riot Units are armed with batons, billy clubs, riot shields and shotguns and will often spawn in their own "riot control" variants of the Lockdown, Bear and Peacekeeper. On the flip side Riot Units move much slower than their SWAT counterparts but they have twice as much health.
At level 4 the FBI and STAG are sent in. The FBI come in two flavors. FBI SWAT who wield M4A1's and can be identified by their green SWAT outfits and FBI Investigators that use pistols and wear navy blue uniforms. As for STAG they look less like stormtroopers and more like a cross between the real-life DHS and military.
At level 5 the Military and Ultor enter the fray. Military forces are comprised of Army troops wielding assault rifles, Marines armed with assault rifles SMG's and RPG's and Navy\Coast Guard\Air Force soldiers armed with SMG's and sniper rifles. For Ultor they look a bit more like the typical Blackwater\Academi merc (short sleeve shirts, baseball caps or in some cases tactical helmets etc) alongside STAG they have access to more high-end weapons the police,FBI, or military.
Ways to loose notoriety: Either A. enter any safehouse\crib or B. Enter any purchased store\property.