There were problems with the earlier World war I model 1903's. The factory workers decided that they could tell by sight when the metal was hot enough for tempering, it usually wasn't, and resulting in bad metal tempering and receivers that can burst when fired. It wasn't caught at first but the carbon can be burnt from the steel from firing over time. It all depends on the serial number. The "official" or "accepted" cutoff numbers for Low Numbered Springfield's are S/N 800,000, and S/N 286,506 for Rock Island. Anything lower than this and it is likely considered NOT SAFE.
I don't believe Remington made any in World War I, but they did in WWII using old Rock Island machinery. The metal problems were discovered by this time and none should have the brittle problem like the earlier models. Make sure the rifle was not demilled for use as a drill rifle. The balance of the 1903 was great for drill teams to use and many were converted for this purpose. As a former NJROTC Drill team member, I have thrown, spun , and dropped a number of them. A drill rifle may be OK for parts but do not use the barrel, bolt, magazine cutoff, or receiver as these are usually cut, drilled, or welded to make them inoperable. Drill rifles can be had for a low price.
As regards value? I've never seen what I'd call a shootable "Cheap" 1903. Even rifles with replacement stocks were going for around $699 from importers like AIM Surplus or J&G. New barrels are still available and the 30-06 cartridge is very popular today. I cannot view your image here at work
but it could be a great project to get yours back into shooting condition. A gunsmith can tell you if the head space is OK or not OK. Its always good to have it checked although its typically not as bad with bolt action rifles as they head space on the cartridge rim, but better safe than sorry.
If you don't want to do it, list a selling price for what you have and I'm sure someone will make an offer for the parts alone.
