Sure I can help you out with the navy but not sure about European ships.
North American (Canadian)
-Iroquois destroyers, has area air defenses and anti sub weaponary.
-Halifax frigates, they uses guided missiles and are helicopter carrying(only one) has surface to air, anti-air and anti-sub.
-Victoria class Submarines, no need to say much.
-Aurora maritime surveillance plane (basicly sees all) armed with air-to-surface missiles, and anti-sub torpedos
-Cyclone helicopters (this is really new to the navy, just released this year and right now only posses 28 of them.) This is a transport helicopter, the only armed thing on it is a Self-Defense gun. It intends to replace the Sea King helicopter.
North America (United States)
-Ohio class, ballistic missile submarine (it carries Trident missiles)
-Virginia class, attack submarine
-USS Gerald R. Ford (or CVN-78), a nuclear powered aircraft carrier, it is classed as a supercarrier (basicly the best aircraft carrier in the world.) It has a Evolved Sea Sparrow Missile (it can destroy missiles and is a AA missile), and Rolling Airframe missile (another AA missile).
- Harpers Ferry class, dock landing ship, it's a transport ship that has a .50 caliber gun, 25 mm Mk 38 cannons it's basicly a large chaingun, and the Phalanx CIWS (Close-In Weapon System) basicly is a anti-ship weapon.
-The Iowa class Battleship, it's the only battleship that can be reactivated in the US navy, this mega super duper powerhouse ship has 50. cal machine guns, 70. cal anti air guns, Tomahawk cruise missiles, Harpoon anti-ship missiles, and a .76 cal Phalanx CIWS.
North American (Mexico)
- ARM Netzahualcóyotl (best if you call it D-102) is a destroyer, the only weapons... Machbox ASROC (Anti-Submarine ROCkets) and deck guns
- ARM Mina (F-214) class frigate, Sea Sparrow Missiles, .54 cal gun, some Harpoon missiles.
- ARM Tormenta (A-302) class missile boat, carries: Gabriel anti-ship missiles, Oerlikon 20 mm cannon, and 2 M2 Browning machine guns.
That's all for North America now I gave you alot of choices so you will have to pick them
Russian Navy
-Graney class nuclear powered submarine, has P-800 anti ship missiles.
-Steregushchy class corvette (long name lol) has a sonar so it can detect subs, 100mm A-190 anti-ship cannon
-Admiral Sergei Gorshkov frigates, ONIK anti-ship missiles, 100mm A-192 cannon, SS-N-29 anti-sub rockets.
-Now Russia has no aircraft carriers today, but they plan on building some next year, but they have the decomissioned Kiev-class Aircraft carrier.
Kiev-class has surface-to-air missiles, 10 torpedo tubes, 2 dual-purpose guns. Can carry 18 helicopters and 12 Yak-38's (now decomissioned).
Europe, now you need to know that there is no Europe Union navy, so each navy is from there country.
France
-Charles de Gaulle (or R-91) aircraft carrier, nuclear powered aircraft carrier and basicly the only one outside the U.S. , Now this one is special cause they have something called the Sylver launcher which is specially built for the Charles de Gaulle, it basicly is a all in one missile launcher (AA, Anti-ship, anti-sub), and 2x 20 mm F2 autocannon guns.
Germany
-Brandenburg class frigate, these are specially made for anti-submarine combat, but it still uses MM38 Exocet anti-ship missiles, and some Sea Sparrow missiles.
Spain
-Agosta 90B class submarine, armed with nothing more but torpedos.
United Kingdom
-HMS Daring (D32) destroyer, has sonar, 2 Phlanax CIWS, Aster 15 and 30 missiles.
Now you have noticed that none of them has battleships because all the countries decomissioned them (It's so complex and expensive, plus they have a really short duration). So you will probably will have to invent something new for the battleships, other than the American ones. I even put up a picture of the only American battleship that can be reactivated just to give you a example of firepower.
Anywho continuing the list
Australia
Honestly they have hardly any ships
-Anzac class frigate, anti-submarine and anti-aircraft
-Collins class submarine, nuff said
-Kanimbla class AMPHIBIOUS transport, Troop & helicopter transport
Japan (or the Japan Maritime Self-Defense Force)
-Atago class destroyers, they use guided missiles
-Takanami class destroyers, uses Evolved Sea Sparrow missiles, 127 mm Otobreda and carries a SH-60J anti-sub Helicopter.
-Shirane class destroyers, this one is special cause it's a helicopter destroyer, uses Sea Sparrow SAM missiles, 54 cal. Mark 42 guns.
-Oyashino class submarine
-Õsumi class amphibious transport dock, only weapons it has are 2x Phalanx CIWS.
China (now China has 2 navies, Republic of China Navy and the People Liberation's Army Navy so I am not sure which one you want me to show you).
Israel
-INS Hanit class corvette, armed with: Barak surface-to-air missiles, a Phalanx CIWS, Harpoon anti-ship missiles, has sonar, radar
-Dolphin class submarines
Cuba (Only two active Soviet ships)
-Former Soviet Union Pauk II Fast Patrol Craft, armed with a 76mm gun, anti-submarine Torpedo and anti-submarine rocket launcher
-Former Soviet Union Osa II PFM missile boats, armed with a MANPAD air defence missile, and a SS-N-2A Styx
Iraq (WTF they have navy? The US and UK are rebuilding the Iraqi navy, so they have 0 ships right now, and the only thing they have right now is this.)
-fast assault boats, (think of it has a terrorist take over of a ship, has % chance of successful controlling the ship.)
Can't help with Brazil, since they won't show me.
India
- INS Viraat class aircraft carrier, armed with 2 Bofors AA guns, can carry up to 30 aircrafts
-Shardul class Landing Ship Tank, armed with WM-18 rocket launchers, and CRN-91 AA 30mm guns, can carry 500 troops.
- Brahmaputra class frigate, sonar,radar, armed with: Barak SAM, 76mm OTO Melara gun, RBU-6000 anti-submarine rocket launcher
There is no Columbian navy.
Argentina
-Almirante Brown class destroyer, carries anti-aircraft guns, a dual purpose gun, and some Exocet anti-ship missiles.
-Espora class frigate, it's really the same thing as he Almirante Brown destroyer but smaller and carries 1 helicopter.
Iran
- SSK Kilo class submarine
- Allen M. Sumner class destroyer, armed with: 60 cal AA gun, 38 caliber gun
Besides if you can't find the names just go the Wikipedia.