Laurel is spot on. Just to back her up and add a couple more comments...
Vatican museum has a ticket which you can combine with Sistine Chapel
(for additional charge)
As she stated, the Sistine is IN the museum so there's no "separate" ticket for it and no additional charge. There is no charge for basilica except to climb the dome and tour the scavi (excavation with the supposed location of St Peter's burial) underneath.
Vatican museum tickets are skip-the-line (if you buy that way!)
Tickets for the museum are purchased by specific time slot and are ALL "skip the line", meaning the ticket line and not the faster-moving security check queue that everyone must pass through.
I read that St. peter's basilica have long queues. Is there a way I
can cover the Vatican museum and then get into St.Peter's Basilica.
What I mean is, Is there a different entrance if I'm continuing from
Vatican Museum to St. peter's basilica?
Yes, but that interior passageway entrance is reserved for tours. Book a tour of museums and basilica you will be able to enter the church more directly. Otherwise you may have to exit the museums and walk around to the main entrance to the church and the security queue there.
Do I save on any time if I continue to Sistine Chapel from Vatican
museum rather than the direct entry?
There is no "direct entry" to the chapel. You must go through the museums to reach it, and it's quite some distance from the main entry.
I'm trying to reduce (or avoid!) my time in line and spend more time
inside the monuments. Any tips?
No suggestions there except to book a tour, maybe. The Vatican offers an inexpensive 3-hour version which hits some highlights of the museums, the Sistine and the basilica, and enters the church through the back passage.
http://www.museivaticani.va/content/museivaticani/en/visita-i-musei/scegli-la-visita/musei-e-collezioni/musei-vaticani-e-basilica-di-san-pietro/visita-guidata-musei-e-basilica-s--pietro-per-singoli-e-gruppi-.html
There are more expensive options which enter the museums before the general public, head almost directly to the Sistine for a less-crowded visit than during regular hours, and then circle back to museum highlights and the basilica. This one has been highly recommended by many RS posters which have taken it:
https://www.walksofitaly.com/vatican-tours/pristine-sistine-chapel-tour
Or this early entrance + breakfast option offered by the Vatican, although the basilica is not included and touring is by audioguide versus human one:
http://www.museivaticani.va/content/museivaticani/en/visita-i-musei/scegli-la-visita/musei-e-collezioni/colazione-ai-musei-vaticani/ingresso-anticipato-ai-musei---colazione.html