Correct, engine swap is exactly like it sounds - you are taking a known good engine out of a donor car and installing it in the target car. You can technically use any 2AZ-FE engine, though it is usually best to stick with the same generation / same model to avoid unnecessary fabrication and modifications.
Not all 2AZ-FE engines have the problem with oil consumption. Some have gone over some extreme distances and don't drink a drop of oil. Others can consume all the oil in the crankcase on a single tank of gas. The real trick is find those 2AZ-FE that won't consume oil - unfortunately, this is nearly impossible to do - as this is not something that can easily be determined. Even if the donor engine doesn't have a history of oil consumption, there is no guarantee that it will never develop oil consumption in the future.
Same with a brand new engine - if you can find them - so called crate motors. No guarantee that they will not eat oil. Factory remanufactured engines (reman) are favored by some, as they usually come with a warranty. Many are clean, used engines that have been lightly rebuilt and verified by factory personnel - usually have updated parts in them, but that is not always the case. Unfortunately, with many of these remans, you can't tell if the parts are updated unless you open up the engine and verify it yourself.
IMO, rebuild is usually the best way to go - you know exactly what parts are being installed, you can see if there are any issues with the engine. Biggest problem you'll run into - is the skill of the rebuilder. If possible, get one that has specific experience with this particular engine, not just one that works on any engine. I've seen guys that have rebuilt 100's of SB/BB GM engines - but doesn't mean they are remotely qualified to work on my engine. Rebuild is also one of the more costly options, given the amount of labor involved in this sort of work. Costs can approach that of a brand new engine - some cases, can even be more costly.
Looking up the value of the car is a good start. Gives you a good baseline to figure out what would be the more viable option of swap / rebuild / junk - time and money-wise.