If you're looking for easy, don't go mirrorless or DSLR.
I'd look as Inon or Sea & Sea strobes. I've used both, and been very happy with them. They're expensive, but totally worth it. If you scrimp on anything, it shouldn't be lighting. Get the best strobe you can afford, or, better yet, two solid strobes. 2 S2000 Inon's will shoot almost anything a beginner would be shooting, and they will grow with you if you ever wish to upgrade. IF you outgrow them (doubtful) you can sell them on ebay for close to retail, as they don't lose their value unless they're flooded or abused.
Sony, Panasonic, Canon and Nikon all have good cameras. I've owned two Canons, and have been very happy with both. I'm a Canon fan, so take what I say with a grain of salt, but I've shot other cameras, and I'd own any of the brands listed without regret.
It's almost time for me to upgrade, so I've been looking pretty heavily at a number of cameras.
I really like the Sony NEX mirrorless cameras. I've shot the 5, and love the lack of shutter lag. The glass on some of the lenses is pretty nice, but you're stuck with whatever lens you strap on for an entire dive. If you put a wide lens on, and then want to shoot macro, you're out of luck. The lens port is also an additional failure point, and the housings are ridiculously expensive (but pretty sexy). If money were not an object, a NEX camera, and a Nauticam housing would be my first choice.
The Sony RX100 is pretty sweet, with a comparatively large sensor. Housings options are better, and cheaper housings are available. The deal-killer on this one is the poor macro performance out of the box. The camera does not focus close-in, and you need to spend additional money, and endure additional complication for macro shots, but I have seen some amazing shots.
I also like the size, cost, specs, and housing options of the Canon S-series cameras (current is S-110). This would be my top choice with my current finances, but the battery life is comparatively poor, which is a deal-killer. If you're shooting in cold water, you'll suffer worse performance with batteries too.
My current pick is the Canon G15 (I shoot a G11 now). It's arguably a top-of-the-line compact camera. It can't compete with mirrorless cams or SLR's, but it has good glass on the front, and it focuses close-in. The G cams have previously suffered from a lack of good wide-angle lens options, but Inon just released a $450-$700 solution to both wide and semi-fish-eye photography with the G-series. This puts it back in the running for me, as the lack of wide-angle was previously a deal-killer.
If you're using 5mm gloves and up, you'll want to avoid the Canon housings. Ikelite housings are good, entry-level plus options for all of these cameras. Fix, and Nauticam housings are available for most, or all of these cameras, but they run about a grand each. They're cut from blocks of aluminum, so they're pretty sturdy, and they hold their resale value reasonably well (though not as well as an Inon strobe).
There are macro, and wide angle wet-lenses available for these cameras as well. That's one of the advantages of a compact camera. You can change from macro to wide angle on the boat, and even on the same dive if you're willing to invest in the lenses. Most of the lenses can follow you to your next camera system as well (like the strobes), which adds value to the investment.
