One of the things to remember is that you often get what you pay for. Yes, it is a 125 yd weapon, so you don't need the optics that you would for a 400 yd rifle.
But, if you check the recoil stats, you will see that the recoil, particularly on a light shotgun like the Ithaca, is up in the elephant gun category. And, in a lot of cases, cheap scopes just won't hold up to that type of recoil. I'd think about buying once, crying once on the price, and then not having to "cry" going through the sighting in pain again when a cheap scope self-destructs and you get to start over.
One other thing to be aware of is if you are using a tapped/screw type base, that a lot of the alloy receivers won't hold up to the recoil. They will fairly quickly strip out the screw holes and your accuracy will go down the drain. I don't know if the Ithaca is alloy or steel, but it is something worth checking.