Hi.
There are a couple of ways one can play retro games with a Raspberry Pi. Most of these are premade images that you flash to an SD card like any other operating system image.
1. Using RetroPie. RetroPie is basically Raspbian Lite with RetroArch (which is used for the Libretro emulators inside of the basic RetroPie install), and EmulationStation, which is the main frontend used to manage and launch your games), in addition to several scripts that are specifically made to work within the RetroPie environment. Of course, you can manually install RetroPie on top of an existing Raspbian install, but it's much easier to just use the premade image. Most of the user scripts that you find from other people are made with RetroPie in mind.
2. Using Recalbox: Recalbox, while similar to RetroPie in that it also uses RetroArch and a modified version of EmulationStation, is geared more towards the beginner side. Recalbox focuses on ease of use as opposed to customizing the experience like RetroPie (things like installing additional EmulationStation visual themes and whatnot), which means all the customizing is done through EmulationStation's menus (Recalbox uses a specially modified version of ES to drive the menus, where you can control stuff like emulation settings, overclocking, etc).
3. Using Lakka: Lakka is just straight up RetroArch with no bells and whistles attached.
4. Using Blast 16: Blast 16 is more focused on Sega consoles, and thus is meant to be used with the MegaPi case from RetroFlag, plus a 6-button Sega-style pad, especially the M30 Gamepad from 8bitdo. It, like everything else, uses RetroArch for the emulation, but as for the interface itself, it doesn't use EmulationStation or AttractMode. It uses its own interface that's really simple. Fun fact, this was going to be used for the upcoming Sega Genesis Mini, but due to time constraints, it was scrapped. Sega really liked it though.

To answer your question regarding accessibility. No, all these options aren't accessible with most screen readers, since the frontends used are graphical in nature, especially if you have a visual theme installed that's very graphically intense. Some parts of RetroPie do use the Raspbian environment for some of the menus, but everything else is ran through EmulationStation or RetroArch, both of which are not accessible. As I said before the only way I am able to use these is because I am low vision and thus have enough sight to use them.

Some EmulationStation themes have sounds, only in the game selection screen though, in that a sound will play when pressing a button to select a game or scroll through the game list. I say some, because it depends on how the theme is made (there are lots of visual themes on the ES Themes Gallery, each made by different theme makers, and new ones are added all the time). How menus work is that the system selection screen is laid out horizontally, while the game selection screen is vertically, though some themes display the system selection vertically as well (note that EmulationStation will only show systems for which you have ROMs for, so for example, ES will only show NES, Game Boy, and SNES if you have NES, Game Boy, and SNES ROMs stored in their separate directories). And yes, the menus do rap around, both in EmulationStation and RetroArch, speaking for RetroPie by the way as that's the only one I ever use.