So, some tips:
1). I highly suggest making another world and spending a bit more time, because each minute you spend in your new fresh hardmode world, the corruption/crimson is spreading rapidly and will until you defeat Plantera.
2). Get a Night's Edge. It is probably one of the best weapons to start hardmode with if you're into Melee. To make one, combine a Blade of Grass with a Light's Bane or Bloodbane Butcherer, a Muramasa from the Dungeon and a Fiery Greatsword at an altar (and keep the Night's Edge -- you can make another awesome weapon with it later!) If not, a Phoenix Blaster will serve you well if you're into guns and bows. Simply get some Hellstone bars and combine them with a Handgun from the dungeon. For Magic users, I am not really sure what to suggest you use, I always found early hardmode weapons to be lacking for Magic users, and found that none of them were really anything I'd write home about.
3). Get either Hellstone Armor or Crimson Armor to begin Hardmode with.
4). If you have Crimson as your Evil Biome, one thing you could do is fish for crates in your hardmode world. You might get a Bladetongue which is even better than the Night's Edge. If you have Corruption, you'll get a Toxikarp instead which.... can be useful in some situations, but I don't think it is quite as good as a Bladetongue.
Either way, fishing up crates lets you get a variety of hardmode ore rather quickly without having to roam around a dangerous world looking for ore spawns. Also, every time you break an altar, you turn one random Stone block into Crimstone or Ebonstone which will cause even faster corruption of your world. Also, smashing an altar triggers impromptu spawns of the Mech bosses, so if you fish up your crates to get your ore and never break a single altar, you will never have an impromptu mech boss attack, though you may want to smash exactly one altar later on so that pirates can naturally spawn without having to use maps once you've defeated the mechs.
5). Try digging a shallow hole in the Frozen biome to farm an Amarok. Just like the Cascade, it can drop off of any enemy in the Frozen Biome. As an added bonus, if a Golem spawns, clever use of yo-yos and hideyholes can let you kill them, and if you get a frozen feather, you will have a free pair of wings once you kill a couple wyverns, rather than spending 2 platinum on Jungle Wings.
6). If it rains, stick around in the Forest biome and try to kill Angry Nimbus clouds, if a Nimbus Rod drops, the Destroyer is laughably easy. Should you succeed in killing it, you can then farm the Yelets from the Jungle, again, using some clever hidey holes to use Yo-Yos or rain clouds to kill the bees there from relative safety.