Traveling by waypoint can be costly, especially if your intended destination is across the map. However, there are a few tricks you can use to save some cash. If you die, you can appear at the waypoint of your choice without paying anything. You will eventually have to pay a repair bill if you rely on that particular trick too often, but it is otherwise useful and pretty affordable. Another option is to enter the The Mists or a World vs World battleground and then simply takea warp to the capital city of your choice. Finally, travel within capital cities is free so you don't have to cross one the old-fashioned way if you're in a hurry.
After you a new character, pick your race carefully. While the various races don't have stat differences, they do have some unique skills they can learn. If you don't care about the personal story or a race's appearence, you might want to take them into account. These skills will be the same no matter what profession you chose.
All professions can support allies and heal themselves, even the Warrior. If you want to play a supportive role in your party, you can do it regardless of your profession, so feel free to select whatever feels better.
Don't always sell your looted equipment to vendors as they don't offer much, and the equipment can be a big source of materials for most crafting disciplines. Once you get out of the tutorial area, purchase a salvage kit and start salvaging them. However, if a lot of the armor and weapons being salvaged are giving you materials easily attainable by logging/harvesting/mining (Copper Ore and Green Wood for example), it might be worth selling that equipment for the extra coin instead. Also, always sell items that are considered junk (name written in grey). As a side note, some cheap items like your starting equipment can't be salvaged.
Using better salvage kits offers a higher chance of getting a stat out of the item and then put it on the empty socket of another. If you find an item with good stats you want, then it's highly suggested that you use your best salvage kit on it.
Collectable items used for crafting disciplines and stats extracted from salvaged equipment can be sent to the bank from wherever you are without the need to be in a City, let alone in the bank. Simply press right click on the item and choose to send it to your collection. Don't let your inventory fill up with this stuff.
Collectable items used for crafting disciplines and stats extracted from salvaged equipment don't take space on your main bank vault. The are kept in a separate place where all collectable items go. Half-finished crafted items, such as shoe soles or staff sticks are not considered collectables and they can only be stored on your main vault.
Upon getting your hands on some gems (by paying real money or buying them from other players with gold) it's suggested that you first increase your bank space. At first glance it looks enough, but it's actually shared with all your characters.
Once you get out of the tutorial you should purchase two of the three gathering equipment (harvesting sickles, logging axes and mining picks). Gathering stuff gives you XP and it also helps with your crafting disciplines. Don't bother buying all three however, since you'll get to choose one of them as a reward in an upcoming personal story quest.