Gyarados

The very embodiment of patience and its payoff, behold the fruit of 400 Magikarp candies. Gyarados's stats definitely help it stand out, boasting great Atk and decent bulk to boot. Historically, Gyarados has been a bit of a sad tale. At its introduction, it had no Water Type fast move, leaving it in a very obscure place in the game; high potential, but no real viability. After about 17 months, it was finally given Waterfall and rose to obtain the title that it had always dreamed about; top Water Type in the game. Then, not long after that, Kyogre appeared and kicked Gyarados off of its throne.

While it's outclassed at this point, Gyarados is still viable, and even optimal in some raids thanks to its Flying sub-typing. It also has a Water/Dark Type Mega Evolution which can bring some great utility for its cost, but even it falls short as an attacker with both of its types. Poor Gyarados is just a sad case at this point....

Best PvE Offensive Moveset

• Waterfall is better than all other fast moves due to its wide coverage and STAB.
• Bite, Dragon Tail*, and Dragon Breath have advantages in super effective matchups, especially when paired with same-typed charge moves to maximize weather bonuses.
• Hydro Pump is the charge move of choice, often equaling the other charge moves in power, even when they have super effective matchups or weather bonus.
• Aqua Tail is less useful than Hydro Pump, but can be beneficial in mitigating Gyarados's energy loss.
• Crunch has an advantage against Psychic and Dark-type opponents, offering the advantage of being a multi-bar charge move and the same typing as Bite.
• Outrage offers a niche advantage over Dragon-type Pokemon, should you fight one.
• Dragon Pulse* and Twister are inferior to Outrage.
• Return has no use on an offensive Gyarados.

Best PvE Defensive Moveset

• Waterfall is slightly better than Dragon Tail* on defense, the former offering better damage against Electric-type counters and the latter against Dragon-type counters.
• Aqua Tail* and Crunch are the Charged Moves of choice for defense, as they come out frequently and have great neutral coverage.
• All other charge moves offer niche situational advantages on defense.

Dragon Breath is a blessing to virtually anything that has it, and Gyarados is definitely no exception. It sports high Damage per Turn and average Energy per Turn, which makes it Gyarados' objectively best quick move despite lacking stab. 

Aqua Tail is an incredibly cheap move that can provide frequent shield pressure. Hydro Pump can threaten KOs when not shielded, but its high energy cost makes it a less consistent option. Crunch provides good overall coverage, decent damage, and a reasonable energy cost, while Outrage is very powerful at a fair cost. This set provides Gyarados with a powerful catch-all playstyle that's hard to come into, and is likely to deal meaningful damage even to Gyarados' counters, while also allowing it to act on opposing dragons while not being hindered by a dragon weakness itself if packing Outrage. Return can be used as a coverage move against Primarina.

You could also go for Bite, with similar performance to Dragon Breath but lower Energy Generation, making Gyarados an aggressive Dark attacker. It is worse against Giratina, however, and with it Gyarados becomes even slower. Waterfall is also not a bad move, and is better against Steel and Fairy Pokemon, but there are generally many superior Water-type attackers to choose from.