Lets focus on the rifle first
Most of these questions are highly dependent upon what the primary use of the rifle will be. Plinking will incorporate different considerations to a large game hunting rifle.
Your criteria: take down large game, 300 yd weapon employment zone (WEZ), affordable, modular, black
I would say a bolt action rifle fits your use best within these considerations.
Most rifles off the shelf today; single and simi, are capable of providing practical accuracy and consistency. Your accuracy will be mostly dependant upon cartridge selection. ie. 5.56, .308, 243, 30-06, etc. As a rule of thumb larger cartridges will be more accurate. So cartridge selection will be the most important aspect of choosing a rifle. Cartridge selection should be based on; WEZ, size of game, availability, and cost.
WEZ
The Weapon Employment Zone is a systematic and comparative evaluation of small arms performance developed by Bryan Litz. It quantifies hit percentage of a given shooting system (shooter, firearm, ammunition) on a specific target. The short of it is, you can buy the most accurate long range rifle in the world with the best scope, however your hit probability will be based on the shooters abilities confidence and ammunition. The ability to read and account for wind, range and velocity will determine the hit probability more than the rifle itself. All in all, this means GET OUT AND SHOOT, track data, and incorporate feedback.
Size of Game
Large game is typically over 300 pounds. This is a very loose number and the terms for game size are muddy as hell. Big game can hurt you, medium game cant, small game is small. A Mule Deer is generally considered the dividing line for medium to large game. Smaller than a mule deer is medium and bigger than a mule deer is large. When taking down large game, shot placement makes a huge difference. A critical hit with a .243 can take down a mule deer, no question about it. Generally the larger diameter of the bullet will give you a larger hydrostatic shock which gives you a larger area of effectiveness.
Availability
What is available in your area? If your ammunition is not readily accessible, are you able to stockpile? Take a look around at what your local stores have in stock, ask them which rifle cartridge is the most available. If they have a low supply stream, it could be subject to going out of stock if a rush hits. Finally, selecting a wildcat cartridge may not be an option. Its could have the greatest ballistics ever, but if you build a shooting system around that cartridge and your supply runs out, you have a paperweight not a gun.
Cost
This ties into availability as well. You can buy online cheaper than in the store, but having easy access to off the shelf supplies will keep you out of a jam. If you choose to stock mainly from the store, thats fine. Lots of people do. Keeping cost in mind will keep your gun fed and keep you shooting. Everyone wants the most accurate round. Why wouldnt they? Buying a .338 Lapua or .408 CheyTac is just out of most peoples price range. Long action cartridges like 30-06 and .300 WinMag are going to be more affordable but more expensive than the short action .308 or .243. Figure out what you are willing to spend on this gun, if you were to shoot it regularly ie. more than once a month.
With your criteria I would look at something in the short action rifle category. .243, .270, .308. They are very popular and widely available rounds and are commonly used by hunters for small to medium sized game. .243 and .270 will give you better performance than the .308 when it comes to trajectory and wind deflection but there is no doubt that the .308 packs a punch. All of these calibers will be effective out to 400 yds depending on what round you choose.
The Rifle
First off, in what situation is affixing a bayonet improving your circumstances? If thats your concern, buy a Mauser for a couple hundred and a bayonet on ebay. You wont hit shit past 100 reliably but hey, you'll always have that bayonet... My advice; get a gun and get shooting first. Worry about cool stuff later.
A short action rifle is cheap new and even cheaper used. If you live in a state that allows personal sales, GREAT! If you dont, most gun stores have a used section that you can look through. I have no experience buying used from a store, so I cant really help you there. As for personal sales, I wont buy unless it fits my criteria EXACTLY. Any deviation and I wont do it. Usually this means I buy it only if its in the stock configuration. New you are looking at under $700. Used prices vary and can settle somewhere around $500 depending on where you live.
My recommendations are; Savage, Tikka, and Howa rifles. They are reasonably priced, have good aftermarket support, well built and accurate.
Savage is the leader of the three in popularity. Dont be swayed by their tacticool offerings, theyre ok but not what you need when you first start out. The mass production aspect usually leaves a little to be desired on the end product. Often it takes a little elbow grease to really bring these rifles into their own. Which costs money. Either in buying the tools, or having the work done for you.
Tikka and Howa are neck in neck for me. They are well priced, within your range of affordability and have excellent fit and finish. Both rifles are going to exceed your abilities as a new shooter and will last. The aftermarket support for both companies is less than savage. However your rifle basics are going to all work. Aftermarket support just means, barrels, stocks, chassis, trigger systems, etc. are not as available.
Remington. My old love... with a heavy heart I do not suggest a Remington. The quality has dropped below the competitors I have mentioned. Fit and finish is sloppy, rust is an issue, accuracy is still ok but you are more likely to get a bad Remmington than a bad Savage.
Accessories
A quality bipod. Its pricey but a quality Harris will serve you well, and your kids well, and their kids well. I suggest the HBL 9-13” model. Its not the fastest adjusting model but it allows fine tune leveling without stepping up into the more expensive swivel models. $75 retail
Scope
This is another discussion entirely.
The down and dirty is, make sure the turret adjustments match the reticle ie. MOA-MOA or MIL-MIL. Dont get wrapped up in MIL vs MOA. If you think in inches and yards- Go with MOA, if you think in centimeters and meters-Go with MIL. Choose exposed turrets over capped turrets. You want the ability to make quick fine tune adjustments without having to worry about keeping track of caps. Taking them off, making an adjustment and putting them back on is a pain in the ass.
Fixed power vs variable power
Starting out, you dont need variable power. A 10x fixed power scope can provide accurate, reliable, and consistent hits at 1000 yds. Fixed power scopes are more reliable and sturdy than variable power scopes. There's less moving parts, which means its more rigid and less failure points. A cheap fixed power will usually be more accurate than a cheap variable power. The moving parts in a variable power scope can introduce unwanted movement and inconsistencies into your point of aim, a fixed power scope, if sturdy, will provide more repeatable accuracy. Variable power scopes are more expensive but allow a wider field of view. This means you can zoom out and track a target, then zoom back in. Thats really the only benefit to having a variable power scope.
Tube diameter
Go with a quality 1” tube. Anything smaller limits the ability to collect light and clarity.
Rings
Go low, the lowest that will fit. Otherwise you will have to compromise your cheek weld or introduce risers, which add to cost.
Reticle
DO NOT BUY A BALLISTIC DROP COMPENSATING RETICLE (BDC redicle). You want to adjust your scope or use hold off to place rounds on target. This will be dependent on your specific rifle and ammo. Anything that deviates from the rifle system the BDC was developed for will introduce inconsistencies. Go with a clean reticle, dont pay extra for crazy lines and measuring tools. Again, make sure the reticle matches your turrets.
Toe support
Get a sand sock to support the butt of the rifle. Cheapest way is to use an old sock filled with sand ie. Sand sock. This will eliminate inconsistencies in the shooters movement and allow you to hold on target longer without fatigue.
Sling
Not that important in my opinion. Unless youre carrying other crap with your rifle, a sling isnt necessary.
Scope protection
Get some scope caps and use them. They're like $10. Whenever your eyes are not looking through the glass, close up your scope.
Practice
When I shoot for groups, I shoot 3 strings of 5 rounds. The average group size is what I use to determine my accuracy. 3 shots is the minimum necessary to determine shot dispersion however, it lacks additional data. If I shoot multiple 3 shot groups and the smallest of them is .8 inches wide, I do not have a sub-minute gun, nor am I a sub-minute shooter. The true representation of my shooting ability is determined by repeatable accuracy (consistency). A 5 shot group may be bigger than my 3 shot group but it tells me more about how I am performing as a shooter. If the string is diagonal (/) then I can make adjustments to my shooting position and trigger control one at a time to bring them closer (l). Then I can work on breathing control to bring the vertical movement in. A three shot group can erratically change its shape simply because of natural dispersion, where as a 5 shot group tells me more about the effect I am having on the gun.
Thanks for reading, GET OUT AND SHOOT
-Kev
Thank you so much! This is packed with info.