If I want the character with HIV to be someone who is well-remembered after his death, then I should I set the story during the 90s in order to have the character die (without very advanced modern HIV medicine)? Or were the HIV medicine during the 90s already sophisticated enough to lengthen the lifespan of someone with HIV?
Well......there's a stigma around HIV and AIDS that persist to this day. People who have contracted HIV via blood transfusions and not immoral means such as gay sex or IV drug use are judged differently.
Royal Commission of Inquiry on the Blood System in Canada - Wikipedia
Those individuals ^^^ were seen as innocent victims and their illness was the consequence of a "corrupt" system.
Then there's Ryan White who was discriminated against because he contracted HIV from blood transfusions:
Ryan White - Wikipedia
BUT....there's also the case of Issac Asimov who was on Reddit's "Today I Learned" earlier this year as being HIV+ from a blood transfusion and his doctors convinced him & his family to hide the diagnosis, possibly so people would still get lifesaving assistance even though this was one of the risks. I've can see both sides of the issue, but I wish Issac A had gone public and helped to reduce the stigma around the disease further just as Freddie Mercury of Queen did. I feel we would be further along, maybe even had a cure by now if *ALL* of the people with power were public about their diagnosis and how they got there.
en.wikipedia.org
Back to your question, in the 90s there were drugs that existed to help manage the disease, treat it - but not cure it - but they were insanely expensive so not everyone who needed the treatments could afford them and there were also a LOT of pills to take at specific times. You may want to research the E.R. character, Jeanie Boulet, a physician assistant on the program who was infected with HIV+ from her cheating spouse, Al Boulet and how she navigated the disease and the medical regiment around the drug cocktail. The musical, "RENT" features characters who are HIV+ and struggle with affording their medications and the rent.
There was also a case in my province, Manitoba, where a family wanted to adopt an HIV+ child from a foreign country and the Manitoba government refused to allow it because they did not want the Manitoba taxpayers to be on the hook for the cost of the person's HIV medications. The newspaper editorials of the day discussed the drugs costing $10,000 a month - health care in Canada is free, funded by taxpayers. This took place around 1990 - 2000 in Winnipeg, Manitoba, Canada if you want to jump into the rabbit hole of researching it. I'll try & find more inform later but may take a while.