Hi Mikkel! Welcome to ChefTalk!
I'm glad to see you are including both sharpening gear and a cutting board in your considerations. That saves a lot of time in the discussion.
But, first, can I ask you where you live? We get inquiries from all around the world, and knife availability is to a very large degree dependent on where someone lives.
Next, about my attitudes. My priorities are about performance first, cost second and looks a distant third. I simply cannot justify Damascus, hammering or kullenschliff (those are the ground-out “dimples”). So, you need to take what I say with that in mind, and if you want any of them, that's your decision.
For the gyuto/chef's knife in your list, I can only speak for two: the MAC Pro and the CarboNext.
I would recommend against the CarboNext, if only for the simple reason that it's not a knife really intended for the beginning chef. It's a knife which is sent from Japan as a blade which is intended for the chef to finish the sharpening process. That's the way chefs and cutlery makers in Japan do it. But not the way Westerners expect a knife.
That's not to say the CarboNext is a bad knife. It's actually gotten good commentary from those who have used it. But the need to work on it before it can be fully used makes it less than ideal for you.
The MAC Pro 240 mm (MAC MBK-95) has long been a regular workhorse and all-around recommended knife. But if this is going to be your first Japanese knife, I would suggest a less expensive knife – the MAC BK-100. It's a knife in MAC's “Chef” series. The steel is exactly the same steel (MAC's “Original” steel), the blade thickness is exactly the same (2.5 mm), the stiffness is exactly the same. The differences are: 1) the BK-100 does not have a metal bolster; 2) it's slightly longer; 3) the angle that the blade and handle have the user's wrist is slightly raised, compared to the MBK-95; 4) the BK-100 costs somewhere about 40% less than the MBK-95 (on discount, the BK-100 is about $110 in the US, while the MBK-95 runs about $185 on discount); and 5) the BK-100 is a bit harder to find than the MBK-95 (not surprising, since the MBK is more expensive and has greater prestige).
I'm sure others will chime in with comments about the other knives and with their individual recommendations.
For a petty, I might suggest a MAC HB-40, which is a 100 mm paring knife/petty, also in the MAC “Chef” series and relatively inexpensive at less than $40 (discount in the USA).
About sharpening gear: I would strongly suggest against any diamond sharpening equipment. Yes, diamonds are harder than steel. But diamonds tend to not want to bond to any adhesive. The only way to hold diamonds is to surround them in a thick surface material that bonds well to the underlying plate or rod. The problem is that the diamonds can very quickly get knocked out of that surface material – at which point you no longer get to use that marvelous hardness.
Instead, I would suggest regular sharpening stones. A 500 grit stone for repairs, a medium stone (800 to 1200 grit) for general maintenance and a 3000 to 5000 grit stone for polishing edges. Try to get stones with a minimum size of 200 mm x 50 mm, but bigger is better.
For a basic primer on sharpening, read Chad Ward here: https://forums.egullet.org/topic/26036-knife-maintenance-and-sharpening/
For some very good videos, watch Jon Broida here: https://www.youtube.com/user/JKnifeImports
For a honing rod, I use the fine grit Idahone. At about $32, it's not too expensive and does honing fairly well.
For how to use a honing rod, read Boar D. Laze here: http://www.cookfoodgood.com/?p=551
For a wood cutting board, the major considerations are size, wood orientation and type.
For cutting board size, the minimum for use with a 240 mm blade should be 18” x 12” (450 mm x 300 mm).
For wood orientation, end grain (where the wood grain is vertical) is better than edge grain (where the wood grain is horizontal). For end grain boards, try to avoid anything thinner than 2 inches (50 mm) thick.
Your preference is walnut, which will work well. But don't overlook the old standby, hard northern maple.
And be sure to thoroughly soak your wooden board with mineral oil before using it (or washing it) for the first time.
Hope that helps!