It depends. The phrases are not synonyms. A good exercise for you would be to look up the meanings of the words.
A "ruin" means exactly that. The structure has been damaged and partly destroyed. The Taj Mahal is a monument, but it is not a ruin.
A monument is usually a memorial to someone, or some event. A useful everyday structure is not a monument. For example, a road, or a chimney that still stands after a house has burned down, is not really a monument. The Diocletian Aqueduct in Croatia is a ruin, but it is not a monument. (If a famous ruin becomes loved and revered, it may be thought of as a monument to the people who built it.)
"Historical" implies that we know its history. We know when it was built, who built it, and what it memorializes. The Lincoln Memorial was built in 1922, designed by Daniel Chester French, and is intended to remember Abraham Lincoln, the US President who ended slavery in the US.
"Archeological" is almost the opposite of "historical." It means it was discovered by archeologists, there are little or no historical records, and what is known comes from detective work and guesswork. This could be true even of something recent. Archeologists might find cellar holes in a woods, and figure out that someone lived there in the 1800s, but not know their names or anything else about them.
Just one comment. English learners sometimes seem to try too hard to avoid repetition. Perhaps it avoiding repetition is more important in other languages. Unless your teacher has given you specific directions, don't work too hard to find synonyms.
If it is really important to vary the wording, remember that once the reader knows that it is a "monument," you can then just call it "the structure" or "the building," or the specific name for whatever it is, like "the temple" or "the tomb" or "the library" or "the pyramid."