Spending gold: Arena or card packs?

What can be won in the arena?

You get up to 5 rewards on completing 12 wins or 3 losses. One reward will be a card pack. The other one to four rewards are random (dust, gold, single cards). More wins = more and better random rewards.

What is the minimum price received when loosing 3 times?

You always get your card pack. The worst random reward is "5 dusts". However, there is MMR matching in arena. You should expect to win at least one game on average even if you're terrible at picking cards.

When accumulating gold through daily's what is the best way spend this gold?

• Dailies in play mode generate 1 pack per ~3 games.
• Arenas generate 1 pack per 5-15 games played.
• Games in Play mode without dailies generate 1 pack per 30 wins (now limited to 1 per day).

There's two extremes of player here: Some players complete the dailies and log off, sometimes going for multiple dailies at once (3 or fewer games per day). On the other extreme, others play at least two hours or more each day (8 or more games per day).

• If you value your time highly (as the first group does), doing the dailies in play mode generates more gold than arenas. Arena purchases wouldn't get used, so packs should be purchased instead. You may want to set aside 300 gold in case you get an extra burst of playtime so you can arena on those days.
• If you value your time playing at a net of zero (as the second group does), doing arenas generates more packs than play mode.

First, there will always be at least one card pack in your prizes. The other prizes are gold, dust or cards.

There is a thread in the battle net forums where players record their winnings in the arena. So far it looks like you need 2 to 3 wins to get the extra 50G back and 7 wins to get the 150G for another arena entry. You get usually about 30 gold for going 0-3.

It seems you get 2 prizes for up to two or three wins, 3 prizes for up to 7 wins and 4 prizes for 8+ wins.

The "best" way to spend the gold depends on your goals.
One important consideration (which was not relevant at the time this question was asked) is that the pack you receive as an Arena prize will be randomly chosen from one of the three existing sets (Expert, Gnomes and Goblins, or Grand Tournament). However, when you buy a pack for 100 gold you choose which set it is from. If you have significantly less of one set than the other two, it is more valuable to buy packs of that set directly instead of "buying" packs through Arena.