How do I go about paying off rental debt that is in collections and ensuring it is erased/shown properly on my credit report?

I am in a bit of a dilemma. I have landed my dream job in another city, which will require me to move. However, I have $2,000 of rental debt that needs paid off. It's in collections and it's about 6 months old, so I know that pretty much will totally prevent me from getting approved at any decent rental property.

Here is a timeline of what I need to do: Once I begin the new job, I will have two months to get to the new city. I'll be remote with them in the meantime. So, I will have the money to pay the collection off in full in the first month. Logic tells me that paying in full will be the quickest way to remove the debt from my report, so I'll have the next month's pay (living with parents in the meantime) to pay for new apartment/moving expenses.

How do I properly communicate with the debt collection agency to ensure that the debt is paid in full and that it is shown as such on my credit report? How do I start this process? I know that debt collectors can be predatory and I don't want to get scammed, or pay it off and not have it reflected on the report.

Would there be a better solution than paying it in full? Am I completely off? I am so lost and would deeply appreciate any input. Thank you in advance!