Starting my first day at Teuida

Difference between 제가 and 내가 meaning "I":

• 제가 [je-ga] - Formal, polite. Used with elders, superiors, strangers. Humble, respectful tone.
• 내가 [nae-ga] - Informal, casual. Used with friends, peers, close relations. Familiar, casual tone.

The ending -겠습니다:

• The ending -겠습니다 [get-seum-ni-da] is used to politely say, "I will..." or "I am determined to..." in formal situations.

제가 하겠습니다. [je-ga ha-get-seum-ni-da]
I'll do it.

• 하다 [ha-da] means "to do"
• 하겠습니다 [ha-get-seum-ni-da]

제가 사겠습니다. [je-ga sa-get-seum-ni-da]
I'll buy it.

• 사다 [sa-da] means "to buy"
• 사겠습니다 [sa-get-seum-ni-da]

제가 돕겠습니다. [je-ga dop-get-seum-ni-da]
I'll help.

• 돕다 [dop-da] means "to help"
• 돕겠습니다 [dop-get-seum-ni-da]

제가 정리하겠습니다. [je-ga jeong-ni-ha-get-seum-ni-da]
I'll organize it.

• 정리하다 [jeong-ni-ha-da] means "to organize"
• 정리하겠습니다 [jeong-ni-ha-get-seum-ni-da]

• A: 이거 누가 하실래요?
  Who would like to do this?
• B: 제가 하겠습니다. [je-ga ha-get-seum-ni-da]
  I'll do it.
• A: 그럼 부탁 드릴게요.
  Then I'll leave it to you.

• A: 커피 드시겠어요?
  Would you like some coffee?
• B: 제가 사겠습니다. [je-ga sa-get-seum-ni-da]
  I'll buy it.
• A: 아니에요, 제가 사오겠습니다.
  No, I'll go get it.
• B: 같이 가겠습니다. [ga-chi ga-get-seum-ni-da]
  I'll go with you.
• A: 좋아요! 같이 가요.
  Great! Let's go together.