EDIT: My reply seems to have become rather long, apologies. Also, apologies if it seems a bit dictatorial and preachy; I am experienced but no expert (there are none?); I just want you to have a good experience of hunting.
I will echo the sentiments in the posts above; the rifle/scope is only the final part of the equation in hunting. Modern rifles and scopes, even at the cheaper-end of the spectrum, are more than capable of the accuracy required to take deer-sized game at realistic ranges (long-range hunting is a bit of a can of worms...)
As with "Bushcrafting", it is easy to focus on the equipment and, in so doing, become distracted from the actual task and the skills it requires. Your rifle needs to function reliably in the conditions and positions you intend to shoot, to deliver accurately a bullet of appropriate construction with enough energy to ensure a clean kill.
Ruger, Howa, Tikka, Sako, CZ, Marlin, Browning, Beretta: I own and shoot firearms from all of these manufacturers and custom made. The only unsalvageable Lemons I have had have been post-Remington Marlins. I bedded my Howa and one of the Tikkas. I have done a lot of trigger-tuning, stock-fitting and "action-slicking" on others: they all shoot and function to my requirements and better. Personally, a Remington wouldnt be my first (or second, nor third...) choice. Savage can be hit and miss, quality-wise, though often salvageable. There are good examples of most rifles, of course, but trends emerge (Rem and Savage not currently flavour of the month).
If you are unlikely to shoot beyond 250m then consider a shorter barrel option. You will sacrifice little in performance but gain in weight-saving and manoueverability. I note you are planning to use a moderator, adding length anyway, and which can offset the recoil and muzzle-blast of a shorter barrel. Likewise, you do not need a heavy-profile barrel: select a light barrelled rifle and the moderator plus good technique will take care of the recoil.
A secondhand gun is always a bit of an unknown: I have several guns that were pre-owned and I have no regrets. Some do not look great through a borescope but still shoot exceptionally well. If these were my target guns, I would be planning ahead for a re-barrel, given the number of rounds shot in quick succession, but as hunting rifles, they usually see only a single shot at a time. Therefore, even if they only have 200 accurate shots left, that is still a lot of deer. I should point out that the specific rifles to which I refer are not barrel-friendly calibres (7WSM for example.)
The question of Calibre is always a tricky one- there is rarely a single, right answer. If you aren't home loading then availablility of factory ammunition is crucial. At a max range of 250m on non-dangerous, deer-sized game, you are not going to have problems with excessive drop or wind drift, nor with inadequate terminal ballistics (within reason.) The excellent 30-06 has been mentioned, but requires a longer action than .308Win and will kick a little more. At sensible hunting ranges the deer will not notice a difference in the two .30 cal bullets, so out of these two, .308Win would be my choice. If you think you might shoot larger animals and/or longer range in the future, 30-06, 300WSM etc. make some sense. It is worth noting that some rifles, eg. Tikka T3, have a standard action length, irrespective of the size of the round.
If you think you might shoot longer ranges in the future, the 6.5mm and 7mm bullets have some advantage over .30 cal (7.62mm) unless much heavier bullets are used in the latter (with knock-on increases in recoil and cost etc.). This is due to the relatively better ballistic coefficient ("slipperiness") of the 6.5mm and 7mm bullets at typical bullet weights, translating into reduced wind-drift and retained energy at range.
6.5mm options would include .260Rem, 6.5x55Swedish, 6.5x47Lapua, 6.5Creedmoor, etc.
7mm options are also numerous: 7x57, 7mm08, 7RM etc. Availability of factory ammo in your area might be a deciding factor.
My general advice to someone setting out on this wonderful journey:
1. Don`t rush to buy a gun (or other kit) Get some experience at a club, ideally with some proper coaching. If you havent shot a reasonably potent centrefire rifle before then you could develop a flinch or other bad habits if a well-meaning shooter lets you "have a go" with a gun that doesn't fit you and which you do not shoot properly.
2. Spend more on the scope and mounts than the rifle. I have never regretted following this old adage. That said, there are some good scopes (with lifetime warranty) at lower prices than previously available. Don`t buy more magnification than you need. 6-8x mag is adequate for most hunting, less if solely woodland stalking, especially driven game. Lower mag means lighter, brighter scope for the money. At most hunting distances, you wont be dialling for wind or drop so exposed/tactical turrets are an unnecessary liability.
3. Practice shooting in field conditions: this is crucial. Range-time is all well and good but there are no shooting benches in the woods nor on the hill! Taking part in competitions that stress positional shooting under time-pressure and with movement is fun and a close simulation of hunting. Learn to shoot using improvised supports, sitting, kneeling, standing and with sticks (quad sticks are incredibly stable and can help keep you shooting above foliage.) Shooting Cinemas can help with this aspect of training. If it is likely you will be shooting running game, it is essential you practice to learn the required lead and technique. In all cases, be mindful of the gun-safety commandments. Dry firing at home can help you to get to know your trigger and how to build a good shooting position.
4. Practice with rimfire club guns, if an option. Learning to shoot a deer-capable rifle is not cheap if you are getting through a lot of rounds. Starting with a rimfire is much cheaper and teaches a lot of the fundamentals of good marksmanship. Ultimately, though, you need to train with the gun and ammunition with which you will hunt.
5. Keep learning, analyse your successes and failures. Keep a log/diary. Dont stop learning and trying to improve but don't get obsessed with kit and upgrades. Sticking with one gun and scope combo yields dividends: "Beware the man with one rifle!" My first centrefire fullbore rifle was a factory firearm with a secondhand Leupold scope. Without modification it has harvested much game and is still used in comps from 50 to 1200yds, even taking Silver at a national level meeting in the McQueens one year (against a lot of custom-rifles.) It is still going strong, sub-MOA accuracy -despite what the borescope says. When it finally looses accuracy, I will rebarrel, and so on until it becomes my son`s or daughter`s gun.
6. Buy some good binoculars: you will use them far more than your scope/rifle. Don`t be seduced by high magnification and needless features. As with your scope, decent exit-pupil is important because much hunting is done at dawn-and-dusk but don't forget that big objective (56mm etc.) also means bigger and heavier bino. You can use binos to focus through cover- this is a really useful technique for woodland hunting. Learn to recognise the subtle texture of fur, visible through a gap in the foliage- this may be all you see of a deer before it sees you. I like binos with a built-in rangefinder- this can be used to hone your own ability to estimate range by taking the binos on a walk when not hunting.
7. Buy a cheap anemometer and use it calibrate your own assessment of windspeed (Arguably not necessary for closer ranges but don't underestimate the effect of wind on bullet.) Bullet drop should be a known variable if you know the range and you have done your homework with your hunting set-up, but wind is not. Reading the wind and compensating for it is vital skill to avoid poor shot placement/misses and to avoid being scented.
8. Practice stalking and moving through the landscape without alerting its inhabitants. Reading the wind direction, avoiding sky-lining, use of cover etc. Electronic ear defenders can be turned-up to exaggerate the sounds of your footfall and contact with brush- this can also highlight how noisy your clothing may be. You can practice this without owning a gun.
9. Know your quarry: identification, behaviour, anatomy, seasons, diseases and welfare. Learn to visualise the animal in 3D: they rarely present broadside to the hunter. What is the likely path of your bullet through the animal for a given aiming point on its surface. You will need to know how to gralloch your animal- though I think there may be compulsory training in Norway? You can start stalking your quarry without owning a gun: get in range and see if you have a safe, clear shot, realistic extraction prospect, shooting position, etc.
10. Respect your quarry, know your limits. Learn what to do if things go wrong and your shot is not perfectly placed. Don`t pressure yourself to bag an animal or you will hurry, take risks and remove the enjoyment of the challenge. A great outing doesn't necessarily have to include a kill. I do not know the system in Norway. In the UK we don't have "tags" or quotas, yet there are plenty of deer, rabbits etc. This means I can hunt a lot (I hunt most weeks), without pressure to fill the freezer (I have three, they are full of game, though I do not bring a deer back each time!)
Most importantly, be safe and enjoy it! I love hunting- it is a primal, instinctive activity that is at my core. Not everyone has this, and so they may not enjoy hunting. It is, after all, ending the life of a beautiful animal.
