most of us are on a tight budget, and you certainly don,t want to spend cash , on something your likely to regret purchasing later, or something in a rather odd caliber that has expensive and difficult to locate ammo.
if limited to a single deer rifle Id most likely try to find a rather common caliber like a 270 win,308 win or 30/06. and personally Id be looking for a deal in a rather lightly used, ... USED rifle, or a lower priced new rifle.
in a bolt action
example (new)
.
https://www.gunbroker.com/item/788967281
if you ask around at most large shooting ranges you'll find a few people with used scopes
or rifles they will sell semi reasonable, the problem will be finding one in good condition at a decent price.
your looking for good value, don,t go by price alone, and have a knowledgeable experience friend check it out,
and I would be very reluctant to buy anything I was not allowed to test fire a couple shots with to verify function.
you might find something like a mil surplus Mauser in good shape, a few years back the 6.5mm swedish mausers,
and 308 win converted spanish mausers were priced well under $200 you might find one that was purchased,
stuck in a closet and nearly forgotten for sale if you ask around,
while it may not be fancy its generally a fine functional hunting rifle