T10 Gear

Sorry if noob question but for T10 gear for priest is it generally ok to pick one set at first but still do both dps/healing? They're kinda similar except for crit/haste/spirit in terms of stats. If so which to pick? It seems to me like the DPS gear is better over all with stats, more haste and crit is better than spirit imo. At least that's what I've read. After all better heals = more efficient mana usage. But then you lose the set bonuses...

Is it really necessary to farm both sets or do most priests who dual spec just pick one or the other set?

If you are DPS then pick DPS set, if you will heal then pick healer set. It's not even primarily about stats, it's the set bonuses you are after.
Sure you can heal with DPS gear and do realtively good, but you will never be picked as healer with DPS set over proper healer.
I can suggest to play with one spec, gear it up, learn it and getting T10/items for your offspec will not be a problem. If you jump from one spec to other all the time you will suck with both of them.