Evidence in favor of 1998:

-Melfi refers to having treated Tony for "2 years" in the finale of Season 2, which takes place in 2000, indicating he'd been in her care since the summer of 1998.

-Tony in Season 3, which takes in 2000, says he's been coming to Melfi's for 2 years, indicating a 1998 date.

-Tony, in Season 4, which takes place in 2002, refers to having came to Melfi for "4 years", again indicating 1998.

-Jackie is not mentioned at all in the Pilot; Tony is referred to as being Boss, and later in a TV news piece on his death, it is said Jackie was first hospitalized "last year" - which could indicate Tony started therapy while Jackie was hospitalized for the first bout with cancer.

-Tony's car registration sticker for all of Season 1 says it expires in 1999. Which would imply Season 1 takes place in 1998.

Evidence for 1999:

-Pussy refers to the seemingly imminent war with Junior as "The War of '99"