Chester

At first, the Chester may seem like a downgrade from the Erie, as your gun range goes down by over a kilometer, your turning speed decrases, and your detection range goes up. You actually have less cannons at hand than in the Erie, since despite having 4 cannons, only 3 can be brought to bear upon an enemy at most. The first few battles will be a pain as you get used to the agility of the ship, and its gun range won't help (Which, as stock, is actually less than your detection range, meaning by the time you can shoot at an opponent, you've already been spotted). You may be pleased by your speed and agility though (slightly hampered by your large size), which is surprisingly good for being so big. The upgraded fire control system is a welcome relief, bringing your gun range to nearly a kilometer above your detection range, which could come in handy if you run into a scary, lumbering tier III ship (Not naming any South Carolina class ships here), where you can use your better agility to scram before coming under serious fire. The hull upgrade will increase your firepower by more than 30%, as you get an additional cannon on each side of the ship. The gun upgrade gives a wonderful boost to your damage output, as your HE shells do a potential 300 more damage, while your AP shells soar a whopping 900 damage up (Remember though that AP can be harder to use, so if you're still getting used to leading targets and knowing when or where to shoot, use HE. Plus you can sometimes light them on fire, which is a rather satisfying event).

If you're top tier, you can afford to be more aggressive. Don't be afraid to show tier I ships who's top of the food chain, though keep in mind that other tier II ships pose larger threats, as tier I damage to you is almost negligible. And always, always, always stay on alert for destroyers. Your large, shiny metallic flank is usually too much for destroyers to resist, and they will always be only too glad to send a torpedo or two (or three) into your side, and subsequently, sending you to the ocean bottom. These, especially the IJN Destroyer, Umikaze, have alarmingly low detection ranges. If you see one suddenly appear, and yet it's turning away from you, it's time to start turning in case of torpedoes. Your agility will help you dodge torpedoes now, but once you move on the the tier III USN cruiser, St. Louis, if you start avoiding torpedoes only when they appear, you've already been hit by them.
If you're bottom of the stack, in a tier III match, be much more cautious. You don't have the guns to punch a hole through anything but destroyers (which are already a pain anyways), and don't be surprised when battleships start running you over with a hailstorm of fire (And they actually could physically run you over if they wanted too). Remember that you are a big target, and that you will melt if you find yourself under concentrated fire. In these cases, never stop moving. You're faster than tier III battleships and the USN St. Louis (Destroyers don't have the guns to pose any threat, just watch for torpedoes. Note that the tier III IJN cruiser, Tenryu, is actually faster than you, and probably has bigger guns. Watch for it.), and if you stop moving, think about what the bottom of the ocean must be like, because you'll be there really soon. You're best off in situations where you won't come under heavy fire, such as supporting the big ships (Usually, the big ships will be the target, as you're not a very large threat), though make sure you're not going to become a major target, as you may have to get uncomfortably close to the other ships (Even with upgraded fire control systems, your range is a meager 9.3 km. Most other ships have ranges of about 10, maybe more.).