My frost specced mage absolutely sucked until he picked up enough talents to start becomming effective. I think around level 24 he had enough talents to reliably kill things efficiently.
I would suggest going for 5/5 Improved Frostbolt to begin with, then picking up 2/2 Improved Frost Nova, then 3/3 Frostbite. Afterwards, go for 5/5 Ice Shards. That puts you up to level 24. Up to level 29, do Shatter. I would do 3/3 Piercing Ice straight after. That's the basic damage talents to set you up for solo grinding. AOE grinding doesn't become possible until some later talents become available though. There are plenty of guides on the necessary talents for AOE grinding around.
As for where to hunt... Honestly, quests are the way to go for me, though I will do some grinding in beneficial places on characters that need something in a certain area, like leather/cloth/ore so I pick a spot for those that I can also gain experience from the creatures nearby.
Normally my order of zones for alliance is this, for humans... Newbie area, Elwynn, all quests up to level 15 in Westfall, then all quests in western half of Loch Modan, then all the rest of Westfall, then the rest of Loch Modan, then a Deadmines run or two for loot and the quests. Afterwards I usually go to Redridge Mountains (at around level 21-22) and do all the quests before I leave, then Duskwood. After that you have a few options and can pick the logical places to progress to, or just follow yours quests.