Private person/firm


When you want to purchase something (for instance like a truck) you can either buy it as a private individual/person or on your firm/company.
How can I say that:
“We can buy the truck…”. I don’t know what preposition to use and whether the terms “private person” or “firm” are used correctly.
Thank you so much for your help.

We can buy the truck on our own behalf or on behalf of the firm/company.

We would like to buy the truck as a private sale.
We would like to buy the truck on behalf of a company.

This will be a prvate purchase.
This will be a business purchase on behalf of … firm/company.