We used One Ocean Expeditions and would absolutely recommend them. We wanted a trip that included the Falklands and South Georgia, a small ship size so we didn't have to take turns on landings and something that wasn't as expensive as National Geographic. Trip Advisor has a pretty good forum on Antarctica. Someone put together an amazing comparison of all the ships that sail to the Antarctic. If is a few years out of date, but an amazing resource.
I’ve been with Hurtigruten and GAdventures. I loved GAdventures and traveled on the MS Expedition a second time to go to Greenland. Hurtigruten was a nicer ship (we were on the Fram), but I noticed the size difference and missed the more adventurous spirit on the Expedition.
I’ve heard lots of great things from Quark veterans and would like to do a trip with them at some point.
Adding a bit now that I have some more time: Any company that’s a member of IAATO can generally be considered reputable.
The only two big things to avoid: 1) a ship that’s still being built. In the past few years there have been some serious delays in new builds, and this has led to entire seasons being cancelled. This is extremely disappointing, and some companies have been better at offering compensation than others. General consensus is that it’s better to choose a ship that has a season behind her already unless you’re extremely flexible with your plans. 2) misaligned expectations. The only people I’ve ever heard who have been disappointed are the ones who had unrealistic expectations. Some people were expecting a more set itinerary and weren’t ready to take whatever came. There’s no guarantee that you’ll get into any landing site, let alone a particular one, and you have to be ready to enjoy whatever the captain and expedition leader come up with. They’re out to create the best experience they can, but conditions don’t always work out. Also, if it’s important that the ship be a certain comfort level, be sure to choose accordingly. There are few to no working class ships, so it’s more an issue if you’re looking for something nicer. MS Expedition is considered a “Medium” comfort ship and it still has cabin stewards and several seated dinners. I’d put it on par with a 3-star hotel. Fram was more of a 4-star.
Beyond that, choose by a balance of price, ship size, itinerary length (and whether you want to include South Georgia and the Falklands), and season if you’re particularly keen on penguin chicks of a certain size. You’re bound to have an incredible trip regardless of the company you end up with. In fact, several of the expedition staff bounce between companies each season, so they’re generally more alike than hey are different!