請改文法～

After much discussion( 經詳細討論後), both of us have agreed to purchase one set each of desktop computer, scanner and database software . However, we are required to submit (我們需要呈交) a proposal concerning the purchace of computer equipment to our college principal for approval .

Hope this helps !

We agreed to purchase one desktop computer, one scanner and one database software after our discussion. We also required to write a proposal on what should be purchased for the approval of our college principal.

After number of discussions, we agreed to purchase one each of desktop computer, scanner and database software. Then, we have to write a proposal on what else should be purchased and to get approval from our college principal.
I'd made it slightly shorter
Indeed, the final sentence (in you text) is not understandable, I wrote with my assumed meaning & hope you would accept it. Thank you.

Further to our discussion, we agreed to procure one desktop computer, one scanner and one license of a database software. To obtain approval from our college's principal, we are required to write up a proposal on what should be purchased.

After our discussion, both of us agreed on purchasing a desktop computer, a scanner and a database software. Lastly, we are also required to write a proposal on what should be purchased to get approval from our college principal.