So, where to start. Firstly I wouldn't worry too much about being infected in the first hours of play, it's only natural to get some damage in order to collect resources. When you have enought consider travelling to every place indicated by the explorer and unlocking the teleportation to those spots, it will grant you more "clean" space to expand. When mining start by collecting everything in the terrain directly underneath the safe spots, then use branch mining to get the amount of ores required to build decent tools (remember to get a smeltery asap to increase your efficency). one big problem is food in the early game, start one farm immediatly and expand it fast, so you can stop worrying about it.
Btw, the purple thing is "the infection" or "taint", The purple land is all infected and the biome is actually called "infected land". the flower simply converts biomes into the original ones, nothing more, by doing so it will make the fibrous taint despawn and clean the land.