It's quite long tbh ? But, you have the 1st three games from the ps1: Crash bandicoot, Cortex Strikes back and Warped. They all connect to each other through a storyline. 1st starts the story where Crash is created by Doctor Neo Cortex and he tries to defeat Crash because he goes against him, 2nd is where Crash helps Cortex, 3rd picks up from there where a time machine allows Crash to collect crystals before Cortex does.
After this a racing game was released (one of my faves) called Crash Team Racing, after this was Crash Bash which is a party game (similar to Mario).
After these the 4th main game (picks up where the 3rd left off) called Wrath of Cortex, this is similar to the 3rd where Crash tries to get the crystals before Cortex does. After this was Crash Nitro Kart which is a remake of CTR.
Then comes Twinsanity (The best). Its an open world game where you travel to different dimensions to get crystals to power the 'Cyclotron'. Its good because you work with Cortex and get to play him, as well as his niece 'Nina'.
Then another racing game was made 'Crash Tag Team Racing'. After this, two more adventure games were made: Crash of the Titans and Mind over Mutant, but these weren't received well as the characters were changed DRAMATICALLY, but now we have the remaster, so its not all bad.