For index downtube shifters, you need SL-7700 if you are using a 9 speed cassette. The left (FD) shifter is friction so basically any FD can be used.
Any SIS mtb RD up to 9 speed and any SIS road RD up to 10 speed can be used, except Tiagra 4700. These are all the original SIS actuation ratio of 1.7mm of lateral movement to 1mm of cable pull.
The shifter determines how much cable is pulled. You need to match the shifter to the number of speeds because the spacing between the cassette cogs changes based on the number of speeds. You can’t just buy 10 speed shifters and only use 9 shifts. The shifters will not pull enough cable to index properly.
John