Hard to tell which older model Ithaca it might be, but I'd chance a guess at a Lewis Model with it's scroll on the sides.
Best way to ID the older ones is by ser#. The Crass, Lewis, Minier (sp?) and even the Flues look enough alike to confuse alot of collectors,,especially the first 3.
Any of these in a 12ga, w/o much case color and refinished wood is not much of a buy at $350 I'm afraid. They are a hard sell in the Field grades unless in excellent condition or priced lower.
High grade guns, they made them up to grade 6 & 7 will create interest of course.
(The Ithaca 'Baker Model' preceded these, but AFAIK was only made as a hammer gun.)
The Crass, Lewis, and Minier are not the strongest actions. The last of them was the Minier,,only made for a couple years 1906/08 IIRC.
Some will be marked 'Nitro Proofed' on the bbl lug.
But what was a nitro/smokeless proof then is not what is loaded now. Take it real easy on them if you do shoot them. Any of these will be short chambered. They were made in damascus as well. Many damascus tubes have been reblued over and it's hard to tell they are in fact damascus.
The Flues was made from '08 to 1926. They still offered damascus in them.
They can handle a bit more than the earlier models but not that much. Same 'nitro proof' thing as the earlier ones.
Small bore light weight Flues are known to crack frames with modern loads. The 12's holdup OK with loads that it's designed for.
The last of the Ithaca SxS was the NID (New Ithaca Double). Strongest of the bunch. Made right up to and for a few years after WW2.
Even a 12ga NID worn colors and refinished wood would probably sit for a while at $350. A few years back it'd be sold in a minute.
Double guns are slow sellers right now.
Just past on a NID 16ga. $375 w/an aftermarket pad. About 75% condition.
Guns w/single triggers and ejectors have buyers. But double triggers and extractor 12ga guns just seem to sit unless priced cheap.
They're just not selling right now unless they're high condition or high grade.
Here's a link to (hopefully) the Ithaca SxS ser#'s. You can quickly find out which Model it is and do some more searching on that particular one. I don't see that they even list the Miniers they made so few I guess.
Double Barreled Shotguns, High Grade Shotgun dates of production doublegunshop.com - shotgun gun firearm SxS Side-by-side
NID's are easy to ID,,they are all in the 400,000 range with their Magnum frame guns in the 500,000 range.