In terms of melee weapons, one of the best ones to get near the start of the game is the bone sword for the extra 2 hits. I'll list the best weapons to get across the game and mention the different weapon types.

Swords: Well balanced with everything and offers good range for overworld enemies.
>Bone Sword. Extremely easy to fulfill the requirements and it's a straight upgrade
>Chainsaw. If you have a high luck/agility build, you can get it's effect much more often. It's a very high risk high reward type of weapon
>Usumidori. Multihits are frankly just better than most other weapons.

Daggers: Always will have a chance to hit multiple times, but has the least amount of range. Prepare to be jumped often.
>Pixie Knife. Pretty strong with the poison effect.
>Sleep Harpe. Multihit weapons and sleep is strange, if the first hit makes them fall asleep the second will wake them up, but waking them up also gives a free smirk. Allows an extra layer of buffer.
>Headhunter . With a high luck/agility build, you can rip and tear through bosses and normal enemies with this easily.

Blunt: Much slower where there is a delay with triggering it in the overworld, but always strong in battle. It's much worse than the instakill weapons for sword/dagger. The only one worth getting is Skull Scepter since it's a strong multihit.

Spears: Offers the most range and the best anti-boss combat ability with built in multihit potential. This leads more of a delay after attacking, which means you can be attacked by the sides if you miss an attack.
>Cursed Lance. Right at the start of the game. Legit the strongest intro weapon in the game.
>Hawthorn Spear. Can be gotten for free and can give sleep, which can be abused.
>Brionac. Always at least 2 hits.
>Dragonfly Slicer. It's Brionac but stronger.

With guns, the best options are the Ace Bazooka, Mikado Custom, and the Gold/Love/Light guns.

Best accessories are the Shot/Power Earrings.