My dad had a 340 Savage for a quarter-century. As mentioned, it is the later version of the 325. His was in .222 Rem and was fairly accurate. He shot it a lot, and by the time I got to play with it, it had lost accuracy. Knowing what I know now, I think I would have tried a couple of things to see if I could get it to shoot better again. He sold it to my uncle and bought a Winchester Model 70 Featherweight in .223.
The 340 is really sort of an ugly cheap rifle. Plain stocks, and lots of sheetmetal. Plus the usual Savage barrel nut. Still, it works, but I never could develop any love for the '50s-era 340, like the love my cheap .222 - the Remington 788 evokes - in spades. That is probably one reason why 788s have double the resale value of a 340. The 340 was not missed by me (or him). Had a neighbor with a .30-30 340, but he was not much of a hunter, shooter, or gun guy. I think another of our neighbor/friends actually shot most of his deer for him with a '06 Ruger M77. Not the gun's fault.
The 340 has a single locking lug, rather than the usual two or more of 'regular' bolt rifles. Less strength, but evidently totally adequate for the lower pressure rounds it was chambered for, like .222 and .30-30 e.g
The other odd thing is that it has to use a side mount scope mount. We are used to seeing this on various Russian-derived milsurps, but it is an oddity with Mauser-derived U.S. bolt actions. My dad had a Weaver mount and never bothered with iron sights (6x Bushnell scope) and was quick and deadly with it. However B-Square makes a side mount for the 340 that allows the use of irons. www.midwayusa.com/viewproduct/?productnumber=146614
Be aware that doing this is somewhat slower - and an experienced scope user can kick butt for speed on anyone who dithers on what to use on close shots. But it fills the need.
The trigger on the 340 was only so-so.
I'm a big fan of aperture or peep sights on stuff like the .30-30 because I think they are more accurate if you figure them out (look through the peep and let your eye focus on the front without conscious effort
). Lever guns are a bit finicky to shoot from the bench with their narrow slab sides that cant easily, and a rest ahead of the lever and not under the barrel is helpful. They seem to shoot naturally from unsupported positions.
Personally, I would keep the lever .30-30, forget the 340, and save for a newer and nicer bolt action sporter rifle in more powerful and flatter shooting cartridge - .308, .270, whatever. Then scope that rifle and you would be set and have a gun that can reach out much flatter and farther. I think it is possible that you can get a good used rifle of this type for around the same price or not tons more - if you shop around. But I have "been there" with the 340 and certainly have my own preferences and likes.
A lot of people who want to mess with reloading the .30-30 with pointed bullets and see how accurate they can be in a bolt gun will buy a cheap used 340 .30-30 to play with.