Please help me either buy, assemble or build a lightweight deer rifle

[Lemonaid]

You did not state preference of bolt action or gas gun or even pistol gas gun. I like the Ruger American Predator--22 inch barrel. "I like it so much, I bought the company!" Well, not really but I do have three of them now.
A gas gun with adjustable length stock might be of use for multi-users of the same rifle. I think it's possible with your budget.