770 is kind of Remington's answer to Walmart's demand for a cheap centerfire. It will shoot, yes. It will kill deer, yes. And if all you want to do is take 4 shots a year, at deer, with a rifle, likely it will do the job just fine.
However, I would suggest taking a look at a Savage. They are known for excellent accuracy and are usually at bargain prices, granted you would then need to factor in a scope. Also, you will get a much better gun, solidly built, and long lasting.