Hellfire Amulet is generally the go-to, since it is guaranteed two good affixes (socket + main stat) and also gives you a 5th passive. To get it, you'll need to farm the keywardens located in acts 1-4 for their Infernal Machines.
The only 3pc/4pc sets left are the crafted ones - all the dropped sets are 5-7 now, with the old 4pc class sets like Vyr and Shadow being upped to 6.
Of the crafted sets, the only ones really worth mentioning are Aughild's (passable filler until you get something better) and Sage's (great for stockpiling breaths, which you can then use in the cube to get something better.) See the theme?
At 16M toughness you shouldn't be having any issues with T6, so have at it. This difficulty will also guarantee more GR keystones, and legendary gems are your easiest way aside from rerolling to boost your numbers quickly while you wait for better gear. Make sure you up to T7 before running bounties though.
No problem
I generally pair classes up with their stat-based equivalent but that's just me. Jewelry like CoE, Unity, RRoG and SoJ are generally easy to transfer, and many weapons can be shared too.