IF you want a new shifter get your choice of 8 or 9 and a cassette to match.
If you go to 9, you'll also need a 9 speed chain, along with the cassette.
Replacing a rear shifter is absolutely the best scenario cost wise, if you want to upgrade to 9.
Your chain rings will be fine re: 8 vs 9 speed.
Don't mix 8 & 9. They don't index the same.