Back when I was into these things hot and heavy, I never found them to particularly unplesant to shoot from a bench rest. But whether they are or aren't isn't a deal maker or deal breaker to me, because I'm not a bench rest shooter. The only thing I use a bench rest for is sighting in, confirming zero, or other similar tasks where I want to take human error out of the equation. Otherwise, I shoot from standing, kneeling, sitting, and prone, and for that, I found little in the full military 1903 Springfield to complain about other than the insanely short length of pull. In terms of felt recoil, if there is a difference between straight, scant, and "C" grip models, I could never tell it off the bench or shooting from it. These things aren't lightweight hunting rifles and don't have the snappy recoil of a light sporter. They especially don't when shooting ammo loaded to duplicate original military ballistics.
I used to shoot mine in matches that would last all day long and during which I would fire several hundred rounds. It didn't kill me. Probably won't kill the OP, either. If he likes the straight grip, then he should get one with that feature and shoot the wee-wee out of it. That's what it was made for.
Now, on the subject of the sights...... A prior poster opined them suited for trench warfare in France, but unsuitable for other usage. I disagree. Strongly.
I wish I could post a pic, but the OP has already seen a live in the flesh example, and if a memory refresher is desired, a search for "1903 Springfield Rear Sight Photos" will provide plenty of visual examples.
And what you should see isn't a tangent sight in the same vien as that on a K98 Mauser. What you should see is a ladder sight, adjustable for windage and elevation, that is foldable to yield a notch-type sight when folded down. When the sight is extended up, it has two peeps to choose from -a smaller round one, with a BIG inverted "V" shaped one above it.
Opinions obviously vary, but I think the 1903 peep sight is VASTLY superior to the issued 03-A3 peep for target shooting and frankly, I wouldn't want either on a hunting rifle when I've got the long slide Lyman M-48 off my old Griffin and Howe sitting in my gun room with no Springfield to mount it on at present. In my opinion, the 1903 peep is more finely adjustable AND it provides a finer sight picture on a bullseye target than the 03-A3 does. People with M-48 Mausers pay to have Mojo sights fitted to their rifles that provide the same kind of sight picture on a blade front sight as the 1903 Springfield rear sight does. Ain't much wrong with it on the target range. That isn't where it "blows." It blows as a battle sight, for a lot of reasons.
I don't own a 1903 Springfield now. As an addict, I can't. Because once I get one, one won't be enough. I have no self control over them. To illustrate, before I got my first Model 1903, the Ruger No.1 was my Holy Grail Rifle. I'm only on my forth No.1 in 30 years of shooting them. I had ten times that many 1903's at the same time once. So yeah, I'm biased in the extreme. Trigger time on the platform didn't dampen my enthusiasm a single iota. In fact, it only made it worse. Much worse.
So I would encourage the OP to give one a try, but do so from an informed position, so that his first one represents a fair deal. As long as you don't get hosed on the first one, if you try it and decide the 1903 experience isn't for you, you can recoup your initial outlay and move on to Enfields or Arisakas or whatever with minimal financial risk. But I'll warn you that the things are addictive like cocaine, though cheaper in the long run and still legal.
JP