The gameplay of Joust is already nicely covered above, but I would like to provide a little more detail on the arcade games themselves
The upright version of Joust was a dedicated cabinet. It is similar in shape to other Williams games from that era, but it is not identical to them (a common mistake that caused me to hold on to an empty Defender cabinet, in the hopes of converting it to a Joust, because I thought the cabinets were identical).
The cabinet is largely black with no painted art on the front of the machine. But it does have sideart, in this case a four color painted rendering of a knight riding a large bird, while carrying a lance. This design is fairly simple when compared to the sideart on other games, and can be repainted by hand, as long as you are careful.
The control panel, monitor bezel, and marquee are all filled with the expected graphics. The marquee especially is a stunning rendition of the Joust logo, and two riders inside the Joust world.
Your Joust machine will come with either 2-Way leaf switch joysticks, or 2-Way optical ones. The early cabinets had the optical ones, while the later ones used the leaf stick ones. In either case it is recommended that you replace those with brand new 8-Way leaf switch joysticks, this will give your game a slightly better feel (from the new sticks), and give you more options for placing additional games inside your cabinet (Robotron 2084 is a popular conversion, and there is also a kit you can buy that will make your Joust into a multi-game with 6 titles).
The Joust PCBs are functionally identical to those used in Defender, Robotron 2084. Bubbles, Sinistar, Moon Patrol, and Stargate, only the ROM chips are different (which was how the multi-game kit for Joust worked).
The cocktail version
The cocktail version (a cocktail game is a sit down table version), is notable because it was one of the most popular cocktail cabinets for conversion to newer titles. You see most cocktail tables originally held games that had monitors in a vertical orientation, and had a set of player controls on each end of the table. By 1985 no one was really making many vertical games, especially not ones that were one player at a time, and could flip the screen for the second player. But the Joust table was different. It had a horizontal monitor, and the players sat side by side, instead of at opposite ends of the table. This allowed the Joust cocktail cabinet to be used for all sorts of newer games (the last time I saw one in person it had been converted to a Neo Geo MVS).
Electronically the cocktail version of Joust was identical to the upright version. The cocktail cabinet did not feature a lot of art, and was mostly black. These sell for big money today. You would be better off buying an upright.
Should you buy a Joust machine for home use?
Probably not. The overwhelming popularity of this title has sent prices far above what they should be. You could probably purchase three other nice games for the cost of a single Joust. You can expect for prices to be in the $600 to $1600 range for a decent machine, and even broken copies will sell for as much as mint examples of less popular games. (You may want to read my writeup in the Ms. Pac-Man node, everything I said there applies to this game as well).