"Vatican City" in Rome encompasses multiple attractions open to the public but otherwise is largely closed to visitors. Of those attractions, two are free (St Peter's Basilica and the St Peter's Square) and others require entry tickets or a tour:
Vatican Museums/Sistine Chapel: advance, timed-entry tickets or a tour is highly recommended as tickets lines can be very long. There is also a tour which includes St Peter's along with the museums/chapel. While the museums can be visited without a human guide, I would suggest at least an audioguide which will help explain what you're looking at. Rick offers audio tours of St. Peter's, the Sistine and the museums which can be downloaded for free to your own device:
https://www.ricksteves.com/watch-read-listen/audio/audio-tours/italy
But if you're interested in a guided tour, those offered though the Vatican's website (link provided below) are as reasonably priced as you're going to find: just € 38.00 per adult for a 3-hour museum highlights + Sistine+ basilica tour, or € 33.00 for a 2-hour tour of just the museum highlights +Sistine. Advance, timed-entry tickets for the museums+Sistine (no tour) are € 17.00. An additional € 4.00 fee applies to all bookings/advance tickets. Any sort of tour or timed-entry ticket can be considered "skip the (ticket) line" but everyone must pass through the security checkpoint queue. It moves along quickly, though.
Vatican Gardens: can only be visited with a guided tour; see website for price. The tour includes entry to the Museums/Sistine at its conclusion but without a guide.
Necropolis of the Via Triumphalis: can only be visited with a guided tour; see website for price. The tour includes entry to the Museums/Sistine at its conclusion but without a guide. There is also a tour which includes this +the Vatican gardens.
Tickets or tours to all of the above can be booked though the Vatican Museum website:
http://www.museivaticani.va/content/museivaticani/en.html
http://www.museivaticani.va/content/museivaticani/en/visita-i-musei/scegli-la-visita/visitatori-singoli.html
In addition, there's the Scavi excavation under the basilica. This also is available only via guided tour, tickets are much in demand, and reservations be made well in advance from this source:
http://www.scavi.va/content/scavi/en/ufficio-scavi.html