First - Every 10 ranks you unlock a new part of the story. Do these, as each branch nets you 30k, which is a good chunk of change to start off with.
Second - Craft. Crafting is an amazing way to make money. If you are just starting off, I recommend goldsmithing as jewerly from the npc is so overpriced you should be able to make a good profit by selling bone rings and brass chokers to other players. (This is how I made 100k in less than 24 hours)
Third - Do guildleves with a group. You can increase the mob difficulty this way, which also will net you bigger rewards!
So, you can only do 8 regional guildleves and 8 local leves in 48 hours. Some of you may think this is a big deal, but it's really not. I will tell you how to make the most of your guildleves.
Do them in parties. This increase your net rewards, and it's fun to play with other people. Maybe you'll even make some friends!
Do ones that offer armor. I travel to all 3 of the cities, and pick up the leves that have armor as a quest reward, and I do those FIRST before finishing the rest of the 8 leves.
Local and Regional do NOT mix. Do some local leves, it's a good way to increase your crafting skills. Make sure you have the proper tool before you venture out into the wilderness though.
NMs - To be contained later.
Random tips -
You can teleport to previous visited aether crystals. WARNING : This will use Anima, which regenerates very slowly over time. Do NOT waste it.
Explore. Talk to everyone. You never know when you may find something useful.
Write down recipes. Sometimes sites like ffxiv.yg.com and eorzeapedia.com are not 100% accurate, whereas you know you will be.
Level jobs you find fun so the game will not get stale for you. Yes, this may be common sense, but you would be surprised how many people burn themselves out because they aren't having fun.
Grind. Go ahead, whine. I dare you. Grinding does the following - Helps you level, gets you elemental shards/crystals, gets you mob drops. You can either sell the mob drops, or use them in crafting. Same for the shards and crystals, which makes grinding a good source of gil. You are killing two birds with one stone.
Well, I guess that's it for now! Hope you enjoyed my basic tips for FFXIV. I shall update this as I see fit, or if people have things they would like to add, I shall include it in the main post and give you credit.