Recently, I've seen a few people talking about how they don't have the credits for their speeder or whatever else they need. I've levelled 4 characters to speeder range so far and I haven't had any problems putting together the 48k credits needed. This guide will also give you some tips on making your levelling life easier.
Step 1: The Gear
As soon as possible, get your self a full set of moddable gear, including weapons. It shouldn't be difficult to collect this either from quest rewards, flash point drops, or even buying it relatively cheaply on the GTN. Doing this means you'll never be coming to the GTN hoping to find an upgrade for a piece of gear that is 10 levels out of date. The second half of this is that you do every quest you can on every planet and always choose the commendation as your reward, unless they offer an upgrade for your regular companion. For most planets, you'll earn enough commendations to fill in every slot in all 8/9 pieces of your moddable gear.
Step 2: How to Level
First, do the PVP daily quest every day. It doesn't give you a lot of experience, but it takes maybe half an hour to do 2 matches and you get a decent amount of experience and credits just from the War Zones themselves.
Second, do every flash point at least once while levelling. This is pathetically easy now with the LFG tool. The daily LFG quest rewards 5 level-appropriate commendations which will help you with part 1, and you also have a chance to get some nice gear drops. You might get a piece that you like the look of better than your current moddable set, or you may get an ugly piece that has better mods in it than one (or more!) of the pieces you are currently wearing.
Step 3: Crew Skills
The obvious thing here is to choose a crafting crew skill that benefits your class. If you're a Force-user, don't take Armstech or Armormeh. Conversely, if you're a tech user, Artifice and Synthweaving will have very little to offer you. I highly recommend that all new players choose Biochem on their first character, because that character will then be able to craft some nice Medpacks and Stims for future alts. I also do not recommend running Crew missions until you get your second companion. This will give you a chance to develop a nice little bankroll before you start blowing through it running your Diploamcy/Treasure Hunting/Underworld Trading/Investigation missions. The last obvious tip is to gather every node you can. There are more crafting skills than gathering skills and if you roll enough alts you will collect extra mats you can send to them to ease their crafting journey.
Step 4: The Alts
Yes, I know the game is new and exciting and you want to try out different things. However, Bioware has designed this game where early altoholism is a bad thing. You don't want to roll any alts until your "main" character has completed Chapter 1 of their story and unlocked your Legacy. The reason for this is, any experience gained by any of your characters on the same server all contributes to your LEgacy level, and there are some pretty cool things you can get with a higher Legacy level. Optimally, you won't roll any alts until you get your "main" to level 50 and have a large bankroll to fund alts with, but credits are easy enough to make in this game that it's not really necessary.
If anybody has any questions, please ask. I am frequently on the forums here and would be happy to help.