I have about 450 gold saved up from daily quests.
Should I spend this on arena or on card packs? The card packs don't guarantee rares for particular classes, right? So I might get something that cannot be used with any of my leveled classes? Do you get cards or gold or what from arena play? Are there awards in ranked play mode (beyond fulfilling quest goals)?
Always spend the gold on arena (your first arena run is free.) In arena you always get a pack plus other prizes depending on how you did. The other prizes are gold, dust, or cards. The cost of arena is 150 vs. 100 for a pack. Usually you'll at least get 50 gold in prize money if you did average (3 wins, 3 losses) to make up the cost difference plus you'll have the fun of an arena run.
If you plan on getting into the game I'd recommend dropping some cash now for card packs. You'll get the greatest return at the beginning vs. later on where you might pull duplicates that are only worth a measly amount of dust.