The current edition of Dungeons and Dragons has a rather large weapon list. However, I there is usually a tendency to focus on particular combinations such as sword and shield, longsword, greatsword and so on. However, there are many other weapons that provide for their own unique options. For this reason, I hope to inspire more variety of use.
The typical go to examples are swords. They are cool, they are iconic and they got good one hand a two hand damage (longsword and greatsword especially). However, many other weapons have the reach property that gives them a bunch of tactical options that swords don't. Shields also give tactical options due to the increase in armor class, but similar things can be accomplished through good armour. The thrown property is also useful, especially so when extra attack isn't present (I let players use extra attack).
Remember, Not Everyone Can Use Swords
I often forget which weapons are considered simple and which are martial. However, this plays a big role. Certain classes cannot use many weapons so remember to keep this in mind when choosing weapons for characters. No one that can use a war pick would want to use a sickle unless in some strange circumstances. However, not everyone can use a war pick. The result is that most non-trained people should be using weapon such as axes and spears.
A player may really want to make a shield and spear fighter but the math of the game moves them away from their desired character. I mean, as written a thrown weapon isn't THAT useful (you can't even throw multiple darts or javelins) but it does give an extra advantage. However, the d8 vs d6 damage of a longsword may be too tempting. If this is the case, a simple magic item can fix this easily. A +1 spear is all that's needed to give the same damage outcome and to make the player happy. Just don't treat it as a magic item and everything is fine (otherwise, the +1 spear has even more benefit over a longsword). You could let the player buy a +1 spear as well. Spears are naturally cheaper than swords in the game so why not a +1 spear? It will still be more expensive than a longsword, so the advantages I feel are earned.
Above, I mentioned how adding a +1 to an item can work. You can also have a custom spear made for the player that has the properties of a longsword but the appearance and piercing damage of a spear. This solves the problem and also doesn't force the player to spend more gold on an item to get what they want and as a result sacrificing other elements of their character.
Brand New Weapons
Some weapons won't be included in the table but are close enough to another weapon. These are easy to add by just describing particular details of a weapon that already exist. You can also add details about particular weapons you are using. It could be that your player is still using a longsword. However, it's not just a longsword now. Now it's a grosse messer or has a ring for hand protection. There is more to a weapon than just damage so don't forget to describe certain things that make your weapon unique. I remember I had one player who had small notches on the blade that all came from important events to the player character's history. It may not directly contribute to combat, but it sure contributes to roleplay and that is equally or more so important (depends on the player, of course).