The core rulebook is the only thing you need, but.
* The physical map (and markers) is a neat thing, but I'm sure the map will be in the book as well. Good to have of course.
* Dice, you need dice. Either buy the alien dice. One set of each is enough, although some rolls might sometimes use more (especially the black (base) dice. Two base sets of dice will be enough. More than that is of course nice but hardly necessary. Also, you could use any dice you have. They need to be in two colours (black and yellow if you want to follow the theme). So if you have 20+ black dice and around 10 yellow just laying around, you can use those.
* 'The cards (initiative cards, gear cards, etc.) makes things easier but are not necessary. All gears are also explained in the rulebook. You can use ten normal playing cards (1-10) for initiative.
“I’d say thistles, but nobody listens to me, anyway.” - Eeyore