There are actually quite a few "alternate" ores and I'll list them. Note that I skip tiers that don't have alternate ores. You'll need to generate several worlds to roll each of these ores, but here's the ones you need to hit. Note that there are armors from other ores and materials if you want to be completionist.
- Tier 1: Copper/Tin
- Tier 2: Iron/Lead
- Tier 3: Silver/Tungsten
- Tier 4: Gold/Platinum
- Tier 6: Demonite/Crimtane
- Tier 9: Cobalt/Palladium
- Tier 10: Mythril/Orichalcum
- Tier 11: Adamantite/Titanium
Note that Chlorophyte will not spawn until you defeat each mechanical boss.
As for finding them, general mining tips:
By far the biggest ore finding aid is the Spelunker Potion. To make it you need Blinkroot, Moonglow, Gold or Platinum ore and a water bottle. This lights up all ore on the screen (playing at your highest possible resolution is a big help with this). It lasts 5 minutes. Making a stack of these will be the biggest single time saver/discovery multiplier you can get. It's not alwys easy to tell the different tints the ores highlight as apart but this potion will radically alter your mining efforts.
Small/Medium worlds require less effort to dig around looking for stuff in. Natural cave networks are a great place to start.
Carry torches, your brightest light "pet", and a Starfury. The Starfury can be used to "probe" dark areas and get an idea of what lies around you. Stars will fall through solid material but then "hit" when they enter into an open area and find a floor. Saves tunneling time and can reveal ore deposits.
Your fastest digging tool is a must. Shroomite Claws are excellent and their shorter range won't matter for basic tunneling purposes. Boost attack speed to taste and go to town! There's only two better digging options in the game, but they're strictly end game stuff.
There is one more thing you can do: use a map viewer program like More Terra. I won't recommend you take this step though if you get frustrated trying to verify which ores you roll in a new world programs like this can at least reveal that information for you. Armed with spelunker potions and fast digging, you honestly won't need a map viewer for anything else.