So, Gold is probably the easiest here In the first century, a Roman soldier would earn ~300 denarii a year, which is about 65g of gold. Purchasing power can be a bit harder to measure going back. In some reports, in 600bc an ounce of gold in Nebuchadnezzar’s kingdom could buy 350 loafs of bread. In Diocletian time a 5g gold could would manage 400 loafs (not perfect math, but that works out to ~2000 loafs an ounce). Take both those numbers with a grain of salt. The Diocletian number is based on an attempt at price controls set to deal with inflation caused by debased currency, so in real life a coin was probably buying a lot less.

Let’s assume the real number is close to 350lbs of bread for an oz of gold. A lbs of bread is also about 1200 calories, or 60% of 2000 calories. So if a Roman soldier wanted a full 2000 calories a day of bread, he would need to spend about 3/4 of his salary to feed himself on bread.

Now, I obviously have no idea how much was in the gift. But a pound of gold was about 5-7 years of salary for a Roman infantryman, and probably enough to buy enough bread to feed someone for a decade.

Frankincense and Myrhh are more tricky. I don’t have a reputable source for pricing, though “worth its weight in gold” gets thrown around. (Aside: a resinous incense grown in Israel - Balm of Gilead - is supposed to be the most expensive agricultural product ever sold, it went for twice its weight in gold). That being said, both incenses had limited sources, which meant that transportation costs (including tariffs and tolls) made up most of the costs, so the closer you were to the Horn of Africa the cheaper you could probably get the stuff.

That being said, given the context of the nativity story, it’s probably safe to assume that even if the incenses weren’t worth as much per pound as the gold, the magi would have brought a bit extra to make it up. ;)

I think it would be helpful to start with an introduction to how we can interpret the historicity of stories like the gifts of the Magi in sources like the bible.

It would be unimaginably great if we had contemporary accounts by perfectly interested but uninvested observers to learn about the life of Jesus from, or better yet multiple independent ones, but the contents of the bible really are pretty much the best we've got for figuring out what actually happened. It was formulated by committee in the fifth century, but that committee did a remarkably good job with the remarkably decent materials they had. The accounts we have are written by true believers, who were not themselves eyewitnesses, and who were writing in a different language and living in a different place than the eyewitnesses. They are also not free from collaboration (With Mark being used as a source for Matthew and Luke), and particularly in the Nativity story they can be pretty wildly inconsistent in both details and global understandings.

However, there is still a lot we can do to come to remarkably solid conclusions out of what we've got. Thankfully there is a common thread among an extended community of puzzle solving oriented people who have obsessed about these kinds of questions for centuries. Since well before the enlightenment, people have been putting a lot of thought into squeezing just about everything that we possibly can out of the extant records we have. They've found that when assessing the veracity of historical materiel, it is important to keep in mind a few more principles, not all of which are very intuitive,

• First, and intuitively, the earlier the sources that the material is found in the better. Even just twenty years can be an awfully long time to be playing a game of telephone, or even for a single person to keep a consistent view of something. We do have pretty reasonable ways to date even the earliest texts, for example each of the gospels refer to the destruction of Jerusalem (even if it is sometimes as an awfully specific prediction) and so we can reasonably assume that they were each written after that.
• Second is the criterion of embarrassment. There are a bunch of parts of the New Testament that really don't fit in the simplistic version of the Christian narrative, and these are, if anything, parts that we can trust the most. Why would anyone make them up later? In a lot of first and second-hand accounts in ancient texts, and including the bible, you will often find things that just make too little sense to be fiction. For example, during Mark's very condensed account of the final arrest of Jesus in the garden of Gethsemane, Judas kisses Jesus, the Romans show up, Jesus gets sarcastic, and everyone but Jesus books it, but then something really interesting happens. Some apparently random unnamed dude, it's not even clear if he was a follower of Jesus, loses his clothes as he tries to flee naked. The naked guy adds absolutely nothing to the story, isn't the least bit relevant to the narrative, and if anything detracts from the message the author of Mark is trying to convey; but heck would that be memorable to an eyewitness. In a time when to be naked was to be dishonored, and to be dishonored was to be less than human in a way that is only really understandable in the abstract in today's world, that was a pretty big deal. While it would never occur to a fiction writer to include this, an eyewitness talking to the author of Mark would have good reason to consider the tale incomplete without it.
• Third is the criterion of multiple attestation, or the more sources we have that cite or repeat the material the better. Material found in multiple sources that are independent of and contemporary to each other is more likely to be historically accurate. It is pretty intuitive that it would be difficult for someone to make something up and get someone else, somewhere else, to make up a similar thing at the same time. Thus many authors saying something in 75 CE isn't necessarily that much worse than one author saying the same thing in 50 CE. For example, both Matthew and Luke talk about how Jesus is from Nazareth but say very different and unique things about how he got there from Bethlehem. Mark also says that Jesus was from Nazareth and so does John, which was written independently of the other three Synoptic gospels. Thus, we can pretty solidly trust that Jesus was from Nazareth. However, as we can assume that since both Matthew and Luke were aware of the prophecies that suggested that the messiah would be born in Bethlehem, their very unique stories of the nativity are probably a result of their common need to explain how Jesus was both born in Bethlehem and famously from Nazareth. The traditional Christmas stories that many of us get as children are generally either one, the other, or a pretty forced mash-up of the two. With this in mind, we can also trust that Jesus did indeed come from Nazareth all the more using the criterion of embarrassment. Nazareth was a two horse town in the middle of nowhere that was famous for precisely nothing and recognizable to practically no one. Particularly when Bethlehem, the birthplace of David, would make a much more reasonable origin for the Messiah as the author of Matthew explicitly notes by quoting prophecy in Micah, why make that up? Even so, how could you possibly get everyone to agree on it if you did?
• Fourth, is perhaps the strongest, basic coherence and just making sense in context. Jesus was an itinerant rabbi in the first century Levant, and any traditions that don't make sense in that context are a lot less reliable. A lot of the later non-canonical Gospels contain things that are pretty wild, but even some of the canonical gospels have some subtle things that don't make sense when you think about them hard enough. For example, in John's account of Jesus' famous late night conversation with Nicodemous, Jesus tells him that he must be born again/above. It is a play on words in Koine Greek, and kind of a neat one. The words used are gennao (Strong's 1080), which means begotten or born in a formal father oriented sense, and it is modified by anothen (Strong's 509), which can mean either again or from above. The author of John uses anothen for both meanings in different parts of the Gospel and so the effect is obviously intentional. However, importantly, while it would have been absurd for Jesus to have been speaking Greek to a Pharisee like Nicodemus, neither the Arahmaic nor Hebrew languages that Jesus could have been speaking have an analogous word with both meanings. Whoops.

What class status would a carpenter like Joseph be in 0ad Judea?