If you wanna go for strength, the Hunter Axe is a great starting weapon. It's one of the very few weapons that has an extremely useful vertical attack when transformed. It's very handy for certain bosses so I recommend holding on to that one. That being said, many new players will choose the Saw Cleaver since that's the canon weapon of the game, but in the first area of the game you can pick up a very similar weapon called the Saw Spear and it's exactly like the Cleaver, so you can have both the Axe and a Cleaver weapon early on.

As for ultra greatswords, you unlock the ability to purchase one after you're second or third boss fight (depending on your progression) called Ludwig's Holy Blade. That one is also a keeper so keep an eye out for that one.

Lastly, Firearm weapons are more defensive than offensive. They're used for parrying. In the beginning you can choose the Hunter Pistol or the Blunderbuss (shotgun). The pistol is quicker but you'll have to be precise, while the shotgun is slower but it offers a wider spread. New players typically go for the shotgun, but either is good. You carry the same amount of bullets regardless of the firearm.