For fastest progress bring good food like cheese or eggplant parmesan, makes a huge difference when you're deep in. Focus on finding ladders instead of clearing floors completely and bombs help tons with that just watch your health when using them. Remember to upgrade that pickaxe early on, the copper one at least before going too deep and check the tv for lucky days (or eat luck buffing food items), way better chances for ladders and good stuff.

Got 100 stone? Make staircases to skip the nasty floors but save them for when you really need them. Killing monsters can drop ladders too and learning their patterns saves your health big time. Every 5 floors you'll get an elevator checkpoint, perfect for dropping off loot when your backpack gets full. Pretty smart to go on rainy days since your crops won't need water anyway and maybe drop a chest by the entrance, saves lots of running around.

Tip for picking professions, miner gives you more ore which is nice early on but geologist doubles gems if you're after quick cash instead. Just remember bombs give mining experience too so don't be shy with them, and always keep an escape route clear when things get dicey.