More than likely, you'll not be able to get away with "just re-ringing" the engine. The reason why is, when the engine was ran without oil and seized the engine, the main part which cause the seizure is the rings on cylinder wall. Due to heat, the rings will grow around the piston until the ends butt together, then the rings start pushing outward against the cylinder walls. It doesn't take long at this point for the rings to grab the bores and stop the pistons. When this happens, it not only causes damage to the rings, but to the bores as well. More than likely there is enough damage to the bores which would precipitate the need to have bores machined oversize. This also would mean you'd need to purchase oversized pistons and rings to complete the work.
You will not know for sure if this is the case until you can get the block completely disassembled and mic'd to see if it is out of tolerance. There is a chance you could get away with a hone and rings, but that's a really slim chance. One of the likely problems with cylinder walls you're going to face in your case is being oval'd out. Whether or not there are large scores from the piston rings, if the walls are oval, it'd need rebored as well. Wear occurs in the piston thrust direction a lot faster under these types of conditions, so it is something to look out for.
Once the block is torn down, you'll also want to measure the rod/main journals on the crankshaft to see where if they are out of spec. At this point, the engine is torn down, so you should check it regardless of oil pressure. If for no other reason, this gives piece of mind. If you're trying to go uber cheap on this rebuild, you could reuse the same bearings. While you could do this, my recommendation is you polish the journals (if not damaged) and put new bearings in anyways. Bearings are relatively cheap and since you've already got the engine apart it makes sense to just change them for longevities' sake.
One of the outstanding things you need to look at in your decisions is answering how long will it take to rebuild the engine and can I have it down that period of time? This depends on the amount of work which needs to be done. If you're going uber cheap, time probably isn't going to be a big factor as it won't take too much time overall to do. If machining is involved, that's going to increase that time dramatically. Replacing the engine with a junkyard one is not going to take near as long, as it is a "Remove and Replace" (R&R) situation, and is usually dependent upon the mechanic's schedule to determine the amount of time.
Another avenue which might be available to you is importing an engine from Japan as a replacement. They have laws in Japan about fixing cars involved in a major accident. Due to this, there are usually a plethora of engines available which might actually be a cheaper alternative than from a junkyard install with a considerable amount less mileage. Here in the States we'd call them a "JDM engine". I've gone this route with good success and for a very reasonable price (cheaper than getting it from the junkyard). We have importers here who bring the engines in so I didn't have to do the importing ... you may have the same in Israel, but I wouldn't know for sure.
Your mention of $2300 for engine and install does not seem unreasonable. If you are able to do the work yourself, you could probably knock a large amount off of the price for purchase of the engine and consumables needed for the install.
You also stated the market value for the vehicle is $4700. Since you like the vehicle, I'd suggest this amount is fairly moot because you have an attachment to the vehicle. The replacement of the engine is well under the worth of the vehicle, so you're not putting more money into it than what it is worth. Regardless, replacing the engine sounds as though it's going to be much cheaper than replacing the vehicle. The money aspect of this endeavor comes down to what your pocket book can stand to support.
My bottom line here is, if it were me with the options available to you, I'd plan on just replacing the engine with the junkyard motor. This is mainly due to the fact you have a high probability the re-ring option (without machining and purchasing new pistons) isn't going to last. It will also save you a ton of time. If you go the replacement route, I'd require two things of the installer/junkyard to do this. First, make sure a compression test is done on the replacement engine and that it is well within specifications. Second, get some type of warranty, where if something goes wrong with the engine, you can get a replacement for it. This might only be six months or some amount of mileage, but still, anything is better than nothing. I would consider some type of warranty to be a litmus as to whether you can trust the mechanic/junkyard as to whether they stand behind their product.
