I have a 10+ years old bike with Shimano 600 (8 speed) which works great but shifters are gone. I need to get a new shifters.
Can I use Ultegra ST-6600 10 speed shifters? Will it work fine?

If later I will want to upgrade to 10 speeds, what would I need to add? Cassette and chain, right? Or something else?

Thanks and sorry for newbie questions...