New brake pads and possibly tires (if the tires look like they're dry and cracked). These will dry out over time, and you'll get much better performance with new. Brake pads are pretty cheap, so its a good investment.
Don't bother replacing the chain unless its stretched (unlikely). All the chain needs is a good oiling. Oil after each of your first 2-3 rides and then ~monthly and you should be set.
Anything beyond that is somewhat optional. Hubs and bottom bracket might benefit from a re-greasing but should be fine without it.