Well first, I would suggest watching our tutorials that you can get to from clicking the link in my signature or at the top of the forums.
After that, the MAME Core in RetroArch isn't bad, but MAME or MAMEUI is certainly an option. There are some small trade offs, it just depends on what you want. RetroArch has some better controller support and shader support, but MAME stand alone may have some better performance. RetroArch also takes some time to update the MAME core (which is just the MAME core by the way and no cores with a year after the name). So the MAME core was just recently updated from .170 to .175, so that was several weeks / months of not being up to date if that's something you care about.
Just make sure that you get a MAME Split set that matches your version of MAME. So if you get MAME .175b from the MAME site (or MAMEUI), then grab a MAME .175 split rom set and you should be good to go. Grab the CHD pack if you can download the giant file size and want the games that will offer.
Make sure to import your games as the system Arcade so that it can properly use the MAME Importer. For better, more detailed help, you should really watch the tutorials. If you have more questions feel free to ask.