I think it's based on the design of the champ. Like, "What are we going for? Is this champion going to be an slow, armored warrior? Or will they be a quick-moving light-footed rogue, slipping in and out of fights?" Once those things are settled, and they have a visual idea (Concept Art and so on) of the champ, then they start thinking "OK, How does this champion fight?" Then the weapon gets chosen.
I personally would like to see some weapons that haven't been used, or at least in some cases, not used in ways I think they could be really neat.
For example:
I would like to see a champion wielding a Warhammer or Maul of some kind, like Shao Khan's hammer/maul, the Wrath Hammer from Mortal Kombat. They'd probably have to be a Fighter or Tank for it to work in terms of their Kit, and if they were to go the Fighter route, it would just make more sense to make that hypothetical Fighter a Juggernaut to match with the massive size of the weapon. If they were to go Tank, they'd probably have to make the champion a Warden, as I would think carrying such a huge weapon would slow them down, and thus not fit for the more "Initiator-Style" gameplay that Vanguards have.
Here's an image for reference:
https://files.cults3d.com/uploaders/13289141/illustration-file/e7c64b6c-d074-456e-b33e-a1be4831885a/Hammer_large.jpg
I know we have Poppy
, who wields a Hammer designed somewhat like this, but I guess what I would like to see is a more BRUTAL hammer user, one that bashes in the heads of his opponents with it. Basically like how Shao Khan uses his, essentially. I'm NOT saying "Just make Shao Khan in LOL", I'm saying make a brutal Fighter (Or Tank, that could work too) who functions similarly, but in League's unique style.
Another weapon that could be neat is based upon an Eku, an ancient weapon of Okinawan kobudō that originated from an oar. The weapon was loosely referenced in Chrono Cross, the sequel to the classic JRPG Chrono Trigger, where the main character Serge used a ornate, double-ended eku as a weapon.
Another image for reference:
https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/7d89d203-d7fc-49a1-b408-1ae10522d873/d81ow8w-4654d36b-815b-476c-ae3e-f9f302c27cd2.png/v1/fill/w_894,h_894,strp/chrono_cross_hd__serge__a_silent_protagonist__by_2playerwins_d81ow8w-pre.png?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOjdlMGQxODg5ODIyNjQzNzNhNWYwZDQxNWVhMGQyNmUwIiwiaXNzIjoidXJuOmFwcDo3ZTBkMTg4OTgyMjY0MzczYTVmMGQ0MTVlYTBkMjZlMCIsIm9iaiI6W1t7ImhlaWdodCI6Ijw9MTkyMCIsInBhdGgiOiJcL2ZcLzdkODlkMjAzLWQ3ZmMtNDlhMS1iNDA4LTFhZTEwNTIyZDg3M1wvZDgxb3c4dy00NjU0ZDM2Yi04MTViLTQ3NmMtYWUzZS1mOWYzMDJjMjdjZDIucG5nIiwid2lkdGgiOiI8PTE5MjAifV1dLCJhdWQiOlsidXJuOnNlcnZpY2U6aW1hZ2Uub3BlcmF0aW9ucyJdfQ.PVLyaGsA8IJAlsQCma_b_zh6GE9ZgRlI0bB0VyXNTJA
Once again, I'm not saying make a champion based DIRECTLY on this character; I'm saying that a champion who wields the WEAPON, or one SIMILAR to it, could be interesting. Once again, he'd probably have to be a Fighter (Probably leaning more towards the Diver Sub-Class rather than Juggernaut) or he could be a Skirmisher.
There are many many more weapon types that could be used, I'm sure, but that's all I can think of at the moment.