Despite being a massive fan of the .243 Win, with which I've taken more deer than all the others put together, I would advise you to step up to a 6.5mm or 7mm and shoot something in the 140-150gr range.
For me, the .243 is a precision rifle I use in quite open country where I can line up a shot with time on my side, so I don't tend to take it into the Kaimanawas or similar type environments. I go with my .308 Win, because I've learnt the hard way over the years that in tighter environments, more weight tends to deliver a more reliable outcome... more forgiving of snap shots, shot placement, intervening vegetation, harder hitting.
Others are sure to disagree! But overall, on the balance of pros and cons, I'd probably select a 7mm-08 for that job. It's a great mid-range option for sika sized animals, you can push a 140-150gr pill at 2800fps+ no worries and that will deal to a deer at 500m assuming you know what you're doing, and you're confident you can find the bastard if it runs.
The three other sensible options include the 6.5 Creedmoor, .260 Rem and of course the .308 Win. Don't discount the .308, I've recently been using mine again after a barrel shortening / suppression / chassis revamp, and I absolutely love it. Any of these four options mentioned will do the job with practically nil observable difference with a 140-150gr hunting bullet.
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