I personally usually recommend Expert Mode for the extra content, but Classic Mode is usually the most optional choice, but that's just me.
But anyway, the best thing to do in your first playthrough is chop some trees, make a house with the wood you collected, a workbench for further crafting, wood walls, a table, chair, a door, and a light source. The Guide NPC you first spawn with will move into your house during the night (he's a very useful NPC so you should always talk to him for when you get stuck).
After the house is built try looking for surface caves and explore them as they usually have chests near the entrance for you to loot (don't forget to ALWAYS pick up the chest you loot for item storage), and during the night stay in your shelter and if you want you can dig a small tunnel underneath your shelter to mine for valuable materials while you wait for day.
