You can play both.
If you need help deciding:
Dragoon is nice and cheap, relatively easy to level, decent solo, good melee damage.
Black mage is expensive, a bit harder to level due to cost and squishiness, but overall a more useful job in my opinion. It'll be a bit rough to fund it as your first job, unless you have good friends.
All other things equal I would recommend Black Mage, for the simple fact that it is a job that will always be in style.
The reason for this is simple; Black Mage is, by definition, the best magical damage dealer. Any other magical damage jobs are hybrids and thus cannot compete on the same level. This means that, unless literally all magic damage becomes obsolete, BLM will always be the first choice when you need to deal magic damage. As well, black mage brings stun, sleepga, and all sorts of nifty little support spells to the table.
Dragoon, on the other hand, is a roller coaster of untouchable and flavor of the month. It's super overpowered, then it's loldragoon, then it becomes buff again, and now it's in another loldragoon phase. It's a great damage dealer, it's just that, so is just about every other job.
WAR, THF, MNK, DRK, RNG, SAM, DRG, NIN, BLU, PUP, DNC are all vying for those "physical damage dealer" slots, and a few of them are always the current flavor of the month, leaving the other ones undesired, regardless of actual potency. Right now, MNK THF NIN DNC are all highly popular due to critical hit builds and the fact that their evasion makes them very durable, WAR is on top of heavy DDing due to Fell Cleave, crit WS, and lots of Red procs.
Dragoon is very good with the crit builds as well but has no real AoE capability and lacks in red !!, making it just another damage dealer, and most of the time, damage isn't really a concern right now. This will surely change in the future, as content strays away from abyssea, but my point is basically that any given melee DD will be a roller coaster between being hot **** and a "lol" job.
tl;dr: Level what you have fun with. If you wanna know what is more practical than my vote goes strongly towards Black Mage, as "Melee DD" are dime a dozen. Being a GOOD melee will still make you stand out, though, so don't let anything discourage you from the job you actually like.
There is no good reason not to level both jobs and play whichever you feel like at any given time, as well. Doing dragoon could provide you a way to farm for your black mage more easily than doing it as you level your first job, but I would recommend having fun with it and not worrying about being the most efficient.
You can probably get by skipping certain expensive/impractical spells like ancient magic, for a little while, but you'll need them for yellow procs once you start doing high level content..
Edited, Jun 26th 2011 5:51am by ItsAMyri