Having actually done this on more than one occasion:
1, It doesn't take oodles of money. I "live 4th axis surface machined" the 2015 SHC rifle stock from a $1200.00 piece of American Black Walnut on a 1992 vintage Haas VF-1. S/N 1762. I just recently donated the machine to the local high school machine shop program. It might have netted me on trade in for maybe $1500 bucks. She'd been around the block more than a few times.
You can buy a fully licensed seat of SW for about $5500. It'll be another $1200 or so for annual maintenance. That's what I pay anyway.
The computer for CAD/CAM use: My advise, avoid Best Buy at all costs. Go to New Egg and build your stuff from scratch. Better components and you avoid a solid day of wiping the drives of all the crap they install. Ensure you get a video card that is endorsed by SW. It matters. A dual monitor setup and a 3D puck mouse ran me right at $4000 give or take a little. -Get a really good battery backup!
Machines: You don't need a 5 axis Makino D500 to do this stuff. Any 10-15 year old VF2 has plenty of horsepower and work envelope to get you going. It's easy to run, easy to talk to, and fast enough to do the job while slow enough for a quick hand to mash the E stop on if things go shitty. The cost is between $10 and $40k. Figure another $1500 to $2500 for rigging. Another couple thousand to wire it up with 3 phase.
Notice I said 3 phase. Phase converters are for home hobby guys. Get in a building with the correct power delivery at the panel. That cannot be overstated enough.
Box way machines like a Kitamura are really nice for cutting materials like steel/TI, inconel, whatever. Rigid, robust, etc. Start cutting on composites and you'll discover that they suck for that. You want a machine with linear rail type ways for composites. Haas does this. A grease pack spindle cartridge is nice too as it'll avoid having Velocite weeping all over your composites. You run stocks dry. No coolant. You don't need a big expensive evac system, but it certainly won't hurt to have it. Diligent maintenance will get you by for a long time.
Tooling: Figure $75 to $200 each for holders. Tooling with be what it is. You can go cheapo import for awhile to get you going, then transition to better stuff later. Remember, its a gun stock, not a Boeing jet.
Hard wire your communications to/from the machine. Wireless does not work worth a shit. Least it never has for me. Shielded cables as fluorescent lights and high amperage cables have been known to corrupt signals during data transmission.
LEARN THE SOFTWARE! If there is anything here that I can offer that I feel is especially meaningful then take what I'm about to say to heart: This is very doable. You can "fat finger" your way through it and make some stuff; at the consequence of having near zero ability to adapt and evolve your ideas as the source code (a very important word to learn and take seriously) becomes left behind. Establish your order of operations from day one and don't waiver. It's far, far too easy to be tempted to just "comp the tool" the extra .04" that it needs for a particular job or whatever. DON'T DO IT. Go back to the terminal, update the model, update the tool path, repost, resend, then go back to work. When the days get going you won't remember all the tribal knowledge. You MUST implement ail-safes to ensure your intent is accurately reflected in the parts your making.
EDIT: As an afterthought. The literal first step in SW is learning how to set it up correctly from day one. A daunting task as there's just so much to fiddle with. Learn the basic format: Plane/Sketch/Feature generation. Build a template and save it as a default part file. Then start with that one and rename it immediately. This way all of your stuff handshakes from day one, till they put you in the casket. Do the same for drawing and assemblies. You Tube is incredibly powerful for learning surfacing and the more organic type shape generation. You can buy CAM systems that integrate into SW almost seamlessly. Nice as you don't have to update your stuff twice when making changes. -Something I really need to do.
Last: The Post Processor. A "post" or "pst" is like a translator. All machines basically run on FANUC G code. However just as folks from Alabama speak differently than a farm kid from North Dakota, a CNC from Haas, Kitamura, etc behaves much the same. The dialect is different. The post is the piece of software that ensures the CAM system delivers the information accurately to the machine. It literally IS the last line of defense. The difference between parts or a spindle friction welded to the the top of a vice. -I shit you not.
Editing posts is a delicate process. It is very tedious and very, very detail oriented. It might be well worth the money to have this done professionally. I cannot tell you the hundreds/thousands of hours I've spent here at work making changes, posting code, then reviewing it to ensure the machine does what I need it to do. Again, I have a mentor that helps when I'm stuck and that resource is priceless. You'd be well advised to do the same.
Good luck. the industry is begging for this stuff right now. A well made composite stock is very fertile soil. . .
A quote that I recently read that I really, really like: "Without facts, you have an opinion." Words to live by, lol.