A good MAME system gives you the experience of all the arcade games of your youth (or at least of my youth) in the comfort of your own home. Arcade games are a pursuit where seemingly-small deviations can make a big difference in the experience, so simulating as much of it as possible is a generally sensible idea.
At its heart, a MAME machine is basically an ordinary PC which has MAME and a bunch of ROM images (probably pirated) installed on it, configured to run automatically on startup and take over the machine, possibly with a pretty front end (since generic MAME is just a long list of ROMs). In fact, I occasionally play MAME on my laptop.
The biggest gap is the controllers. A mouse and keyboard can't even simulate badly most of the controllers from most of your favorite games. Using a mouse as a trackball for Centipede is hopeless; even using a trackball intended for PC work with it is not great. A modern joystick suitable for playing a flight combat game is bad for Time Pilot, worse for Pac-Man, and hopeless for Robotron. And there's nothing in the world that'll do for Tempest other than a proper spinner. (I have a standalone Tempest spinner, but the problem is, you need the button, too! And it has to be in the right place.)
You can buy arcade-style joysticks and buttons and spinners and everything else you can imagine, and build your own control panels. It can get pretty complicated and expensive, though. Building your own panel that can control everything becomes a complicated act of wiring since you don't want every device to have its own USB connector. Most MAME enthusiasts spend as much time on collecting and building their machines as playing them, but my goal is to take a middle ground; I'd rather spend 1/3 as much money and do some building, but I don't want to be building at the component level. So I'll buy a pre-built, everything-in-one control board like this one. You can even just hook that to your PC and start playing. It's a little crowded (a panel which you could swap out controls from would be ideal, but no one makes a prefab one) but the arrangement looks quite workable for just about every game.
Going from there to a dedicated machine in an arcade-style cabinet is probably not as big a step in achieving the playability part of the arcade experience, but it's still a big step and one I hope to take this summer. Again, you can build your own case from plans you can get online, or your own plans, or you can buy an assembled case, or a kit. The latter is probably how I'll go, once I work out some details about how the controller mounts on the case, what kinds of monitors I could use and how they'd mount, and what components are required and which ones are just "jazz" or just simulations of the arcade that don't matter to me -- like the lighted, and possibly working, coin slot door -- I'm not in this to collect quarters!
I don't know if I'll get to do this this summer as planned: the summer itself is going to be busy with travel and other projects, and my budget is likely to be tighter than I anticipated due to the travel and a few other purchases. I should at least get the control panel, but not sure yet about the case. Unfortunately the act of figuring out what I'll need has gotten me excited about it and I want to do it now! Oh well.