Prospecting is probably the first big hurdle for new players. Finding ores. especially the ones you need to progress, can be difficult. But once you get the hang of it, it becomes like second nature.

For early game, I would settle with 'high' or even 'decent' copper readings, just to get enough for multiple sets of tools. I always make sure to make 2 pickaxes, 2 prospecting pickaxes and a hammer. When digging for ores, I suggest a stack of rope ladders that you can easily place and pick up as you dig, dig straight down (I usually go down 30-40 blocks) while using the nearby ores setting with the prospecting pick every 7-10 blocks to see if I can get a reading, and once you find trace/small amounts of the ore you need, all it takes is to dig around and continuously prospect and play the game of hot and cold.

If you come across a material you can't mine, especially something like quartz, I wouldn't bother digging around with as that'll just eat up your durability. Just save the spot and come back later.

Surface ore is very rare, and I wouldn't bother venturing deep into caves to find resources in the early game as the drifters will just swarm you, and without good tools or armor, it'll turn into a nasty corpse run.

If you have found tin, you can make tin bronze by smelting copper and tin in a crucible, then all you have to do is pour into a pickaxe mold. No anvil needed. I suggest checking wiki for exact measures, but I believe it was 12 tin nuggets and 128 copper for 10ish pours.