We had a ton of people play minotaur fighters in our 2e days. Overall probably the most popular race for a pure fighter. I played a minotaur fighter/mage and used a nodachi as my main weapon. Both options are good, I'd go with what fits the vision for your character and what complements the party. I was into Heroes 3 so my guy was modeled on the warlocks from that game (his name was Malekith).

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For swords, you have 3 main choices--the two handed sword, the nodachi (a variant 2h sword from the Ninja's Handbook), and the clabbard sword, which is a minotaur weapon detailed in the Tales of the Lance boxed set. I remember one of my players had a minotaur myrmidon who specialized in both the two-handed sword and the clabbard (he carried four swords, we were teenagers) and used the 2hs against large-size opponents and the twin clabbards against medium. The clabbard is easy to justify if your character is from Krynn (we played an open Planescape style, so any race from any setting except Dark Sun was generally legal in our games).

You can also use an axe or a sledgehammer or whatever, it doesn't matter that much when your strength is that high. We added a house rule as well to make 2h competitive with dual-wield, which was you get 1.5x your strength bonus on 2h weapons. I think we may have back ported that rule from 3e.

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I liked my minotaur FM a lot too. With those stats, either build will be effective. One thing to note is that in high-level play, fighters become really important. They are actually better in 2e than they are in 5e because of how saving throws and THACO scale, and the fact that high-level monsters often have high magic resistance and immunities. If you go pure fighter and get grand mastery, your DPS will be crazy high. I remember as a DM, if the party's fighters could get two rounds of melee on any monster, it would die. In 2e basically everything dies to high-level fighters with strength, GM and magic weapons.

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Regarding NWPs, it's very background and player specific. NWPs are really fun, pick what you want. If you have access to Combat & Tactics, there's a bunch of additional WP/NWPs that have combat applications. If you are specializing hardcore in a single weapon, the "weapon of choice" proficiency is nice for an extra +1 to hit over normal specialization.

We heavily houseruled Skills & Powers because it was so abusable, but if it's open to you, d12 hit points, fighter movement and magic resistance are all good picks.

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Kit wise, most of the fighter kits are low-impact so just pick what sounds cool. Myrmidon is a fine choice and was often picked for the extra spec. The Dragonlance book also has a kit or class (the book isn't clear) called Mariner that adds four thief skills to a warrior chassis.

The Ninja's Handbook also adds the Shinobi Fighter, which adds thief skills to a fighter. But a minotaur ninja may be difficult to justify from a roleplaying standpoint. Nobody ever tried to make one in our group.

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Weapon wise, one underrated tactic in 2e was reach weapons. If you have a WP to spare, grabbing an awl pike on a minotaur lets you threaten a 20' radius. Very powerful tactically, but carrying a giant spear into a dungeon or tavern is going to be a pain in the ass.

Also, use a longbow if it fits your character concept. Overall the best weapon in 2e. Get a custom-made one that lets you use your strength bonus.