help with first time pay raise negotiation

i have a meeting with my supervisor tomorrow morning to discuss my hours and compensation. this is my first real job out of college, i have been in this role for 3 years working 20-25hr / week and i’m hoping to raise that to 25-30 hr and my pay by $5/hr.

i feel like this is reasonable given how my responsibilities and skills have expanded since i started, how much the company (startup) has grown in the past year, and also because i know i’m paid less than my coworkers by at least a few dollars an hour. not to mention cost of living has gone up so much recently this is what i need to make ends meet. however i’m really nervous about coming across too entitled/greedy or saying the wrong thing and being let go

Please explain like i’m scared:

1. how do I phrase this reasonably and professionally?

2. do i need to bring specific examples of my work to justify it?

3. should I ask for a higher increase than what I need expecting them to negotiate down, or will that reflect poorly on me and I should ask just for what I need?

4. is there anything else i should expect or be prepared for in a meeting like this? for context my supervisor invited me to talk about it himself

thank you