I think I have some definitive answers for you.
The Matrix isn't really optimum, because you can't trigger a one-shot properly. It's designed more for looping, so you have to hold the trigger key down for as long as you want the sound to last if it's not a loop. Nor can you really record the "hits" properly as MIDI triggers.
Session Drummer does the job very well, but it has only 12 channels audio instead of the MPC-style 16 channels, and the drum layout is disorienting if you're not doing something drum-related. However, each channel can have more than one sound (for example, the kick can have two separate samples triggered by different notes). So if you don't need separate outputs or processing for every sample, this will take care of you. If you do, insert more than one Session Drummer.
Another option is Cyclone DXi, which is ancient but is the closest to "MPC-style thinking." It lets you drag samples on to pads, trigger them as one-shots or loops, and more. There are two big drawbacks that may or may not matter: The pads don't respond to velocity, and they don't have a MIDI learn function (although you can change them manually to respond to particular notes and channels). If you just want to trigger samples and don't care about velocity response, this is the fastest option.