I would appreciate it if someone would hook me up with a manga that the character is transported or reborn into a new world where he/she can level up skills and must level up themself to get stronger.

if you mean stuff that has semi natural progression and he is not high level just because, yeah, that'd be nice.

rise of the shield hero fits teh bill for a decent amount of arcs.

Reincarnation Dump!
Some of it's exactly what you want, some of it's close:

Mushoku Tensei - Isekai Ittara Honki Dasu
E? Heibon Desu yo??
World Customize Creator
Gunota ga Mahou Sekai ni Tensei Shitara, Gendai Heiki de Guntai Harem o Tsukucchaimashita!?
Re:Monster
Shiro no Koukoku Monogatari
Tenseisha wa Cheat o Nozomanai
Spirit Migration

________________
Looking for something different? Try one of these:

Otoyomegatari
Dungeon Meshi

Any more besides the ones listed above?

I did some digging for you and found these:

Hai to Gensou no Grimgal
Megami Ibunroku - Persona
The New Gate
Yakushoku Distpiari - Gesellshaft Blue
Toaru Ossan no VRMMO Katsudouki
Helck
Dungeon ni Deai o Motomeru no wa Machigatte Iru Darou ka

^^^I have NO idea about any of these as I haven't read them myself.^^^


Also one I forgot to mention:
Overlord

________________
Looking for something different? Try one of these:

Otoyomegatari
Dungeon Meshi

Tales of Demons and Gods - Same world however he is reborn back in time when he was a youth. When he was older, he didnt have the power to protect the people around him. Since he has been reborn, he tries to level up to grow stronger and change his future.

If u read novels
Against the Gods (Novel)- really good reincarnation story. THe main character is looked down on and is despised. A underdog story where he strives for power and levels up.