Planning on going hard with both PvP/PvE what professions will I get the most out of. 
Probably Tailoring and Engineer for both. Bombs repair bots Bloodvine is BIS till Naxx if you are 300 tailoring IIRC
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As a gnome mage, The engineering dragonling trinket, iirc, makes it lvl 63 which makes it much harder to hit in pvp. Tailoring works well in pve with the crafted high end gear.
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Min/eng. for the max lulz in pvp. Although, tailoring is sexy for zg gear.
Might need an alt or 2 for max effiency.
If you want to PvP then you need engineering. If you want engineering then you need mining.
You’ll need multiple characters then. Tailor/Engineer for main, like @Pintero said, but you’ll need a herbalist/alchemist to make pots, and a miner/blacksmith to make engineering parts and provide your bars.
Gotta go mining / engineering pal.
Anything less is just a waste of a perfectly good gnome.