Most any rifle is "capable" of 1000yds, it just depends on how much time, money, and effort you want to put into it. That being said, there are a great many Savage rifles out there with minimal modifications shooting to 1k. Obviously as you stated, an optics upgrade is a must. That is a rabbit hole of debate as far as which is best etc etc but don't be afraid to spend money on glass and mounts. Cheap mounts will make even the best scope be at risk for POA failure when you need it. Rule of thumb many people follow is spend 1x to 2x the amount you paid for the rifle on optics/mounts (just as a general rule of thumb, and of course there are always exceptions to the rule).
The 7mm Rem Mag is a popular and quite capable cartridge that with the right loads can take on almost everything you would ever want to hunt in North America.
If you are comparing this model 16 to your prior Rem 770 then you will be in for a very nice surprise. The Remington models 710 and 770 (basically the same rifle with the 770 replacing the 710) are for all purposes trash. Very cheaply made, wear out quickly, not usually very accurate. Many new shooters bought these because it wore the Remington name and lived off of the fame of the model 700, however it could not be further from the 700. If you want a truck/atv gun that you know you're going to destroy a 710/770 MIGHT be up to that. I tried to help people in the past that owned them and eventually had to explain that it is what it is. Got most of them at least switched over to an Axis since many of them need to stay at the entry level financially speaking.
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