I think a lot of people would agree on a mid caliber (25-27) semi-auto. Actually, an SKS in 250 isn't as tall an order as one might think.
For me, I have to fall back on the 30-06. Here's my "ultimate rifle":
First off, although my state prohibits the use of semi-auto rifles for hunting, I would want my ultimate rifle to be semi-auto. A reliable semi-auto is more consistent in reloading than a human operating a bolt, since the speed would vary no matter what.
Second, while many excellent and reliable semi-autos are made with stamped parts, this one should be machined. If I were trying to produce this rifle for profit I would consider a stamped receiver, but the best machine design optimization requires regulating every dimension, keeping material where it's needed and removing it where it isn't. In other words, you can sometimes get the best rifle for your money with a stamped receiver. But the idea here is to get the best rifle period. My idea of a receiver for this type of rifle would be a two part receiver. The upper would be steel with machined rails and the barrel screwing in at the front. The lower would be aluminum with the magazine well and trigger group. It might look like an AR style at first, but the lower would also serve the same purpose as an SKS dust cover, namely keeping the bolt and carrier inside.
The cartridge I would choose - 30-06. Almost every army in the world adopted a cartridge with similar ballistics to this one at the beginning of the 20th century. In the mid century, a certain load for it was almost matched with the shorter 308. But the whole range of loads available for the 30-06 cover a much wider range of performance. Reduced recoil loads with 125gr bullets are common, heavy 220gr hunting loads are too, mid range loads of 150gr and 180gr bullets are omnipresent, and then there's Hornady's light magnum, which should not be used in any current semi-automatic. Military ammo is still out there, and now that 7.62x51mm NATO has jumped in price, 30-06 is almost equivalent economically. Never mind that you can reload a good bit of the 30-06 brass out there.
One thing this rifle would absolutely need is an adjustable gas system. No question about it. With clear settings for reduced recoil, military, sporting, and light magnum loads.
With adequate machining, this rifle could feasibly be no heavier than the sporting semi-autos by Remington, Browning/Winchester, and Benelli. I could very easily, however, tolerate a modest increase in weight. If possible, it shouldn't be too much towards the front of the rifle. I'm thinking 10lb max, or perhaps that much fully loaded.
For a magazine, BAR mags would be the standard. However, smaller mags would be useful when you wanted something more compact or flush with the receiver. So fresh 5-10rd mags with the BAR latch pattern would come wiith the rifle.
I'm very torn between having an open top to the receiver, like the SKS and M1 Garand, and having it closed like practically all rifles that load from a detachable mag. I would like to be able to load the rifle from the top, especially in a hunting or other sharpshooting situation. But the strength advantages of a closed top receiver are significant, both for safety and for the rigidness of optics. With an open top receiver, I'd be inclined to use a scout type mount, but I don't have much experience with that setup myself.
Another thing I'm torn over is having the piston above or below the barrel. Above would be sleeker and more modern, but below would have its advantages. Above would be like an FN-49, below would be like an M1 Garand. A piston below the barrel would allow for an AK-type long stroke gas system, which is my preference, and allow for an open top receiver. A piston above the barrel would either have to be short stroke, like the SKS and FAL, or if long stroke it would cover the top of the magazine and require a closed receiver.
The bolt would be something we don't see much of - a four lug bolt with 45 degree rotation. To me it seems an obvious choice. But no, everyone instead uses a 2 lug, 3 lug, or many lug design. The four lug bolt would allow it to ride in the receiver on two lugs like an AK bolt, have a 45 degree lockup like the AK bolt, and have superior strength. I'm torn between a fixed ejector and a button ejector, but I'm pretty sure a lever-claw extractor is what I'd want there.
For a stock on a do-everything rifle, I wouldn't want a protruding pistol grip, instead I'd want a classic stock with a more vertical grip than usually found on a sporting rifle. If it had an underbarrel gas system, it would have to have a full length stock, in which case the main external distiction between it and the M1, besides the trademark receiver profile, would be the detachable magazine.
If I really wanted a p-grip stock I could have an additional one, and with no springs in the buttstock there would be nothing preventing you from making a folding stock, vs the AR which has the buffer tube in the buttstock.
I'm not sure about the sites. A maximum site radius would be great, from the rear of the receiver to the muzzle, but I like the profile of having the front site on the gas block, like the FAL. The muzzle could be threaded for a common muzzle attachment, and you could keep a variety available. They could include a muzzle brake for minimizing recoil, a flash hider when you cared less about recoil than muzzle flash, and then varieties of each. Even a suppressor if you decided to go NFA.
So would any of you want something like this? Or what would your "ultimate rifle" look like?
