In short:
7 speed: Altus and lower. What you have now.
8 Speed: Alivio. You can use existing 7 speed cranks, FD and chain.
Just change cassette, RD and shifter/levers (EF29/35), there are some good road cassettes in this range.
8 Speed Sora. You will need to change the FD and Crankset, BB,
cassette and RD. Still use existing chain, if HG. Use 443 levers and shifters.
9 speed: Deore. Change everything, Crankset, FD, BB, RD, Shifters,
cassette, chain. Cheaper to change bike.
9 speed: Tiagra, Change everything, Crankset, FD, BB, RD, Shifters,
cassette, chain. Again, cheaper to change bike.