Gen Urobuchi has stated that Black was a huge influence on Gaim - specifically, the duels between Black and Shadow Moon were what influenced the show's writing. Plus, Kouta is very similar to Kotaro, and Shadow Moon has a counterpart in this show as well (I cannot say who as that would spoil things).
Both have a darker overall plot but are very episodic with a lot of the episode plots being silly one offs. Lupat is sillier while black has a darker ending
While RX is a lighter show it is still the direct sequel to black so if you want to see the next part of the story for our Kamen rider watch RX
Black is the series after Super-1 so if you want to watch the Kamen Rider seasons in order watch Black after Super-1.
After being kidnapped by the cult Gorgom on the night of their 19th birthday, stepbrothers Kotaro Minami and Nobuhiko Akizuki were submitted to a cyborg surgery with the purpose of becoming the candidates for the next Gorgom Creation King. Both of them are called Century Kings and are destined to best each other in a final battle - whoever wins will become the next Creation King. Kotaro escaped before getting brainwashed (which is the final step in the surgery), with help from his foster father, and turned against Gorgom. He soon finds out the horrific truth from his stepfather: Gorgom originally killed his true parents and, since both Kotaro and Nobuhiko were born on the day of a solar eclipse, referred as "Black Sun" and "Shadow Moon". Kotaro, taking on the name of Kamen Rider Black, was determined to rescue his stepbrother from Gorgom while protecting Japan.