The Sistine Chapel is part of the Vatican Museums and covered by the same ticket. St. Peter's is free but with a regular ticket to the Museums you must exit and walk around part of the exterior of the Vatican complex to reach the door to the basilica, where you will find a shockingly long security line. The basilica opens at 7 AM most days, I believe, and conventional wisdom has it that showing up super early will mean a much shorter security line. I cannot vouch for that because I am not a morning person and didn't manage to get to St. Peter's last year.
Some tours that include both the Museums and St. Peter's are allowed to take their clients through a back door between (or near) the Sistine Chapel and St. Peter's. That is a huge time-saver, because you avoid the walk and the security line. However, there have been occasional reports from tour clients who were unable to use that door, so it's not something you can count on 100%. There's also the issue that to use the door, you have to leave the Sistine Chapel/Museums with your tour group. If you want to backtrack and spend some extra time in the Museums after your tour moves on, you will not have access to that special door. The Vatican itself doesn't offer combination Museum/St. Peter's tours, but some private companies have done so in the past. They include Walks of Italy.
The Museums have changed their entry procedures and their tour offerings this week, so it's hard to know how the new options will work out (and I didn't take a tour myself, anyway). This website will list your choices after you choose your preferred date of visit and the number of tickets needed:
https://tickets.museivaticani.va/home/calendar/visit/Biglietti-Musei
The Museums are usually closed on Sundays. I think (not sure) St. Peter's is closed for tourist visits on Wednesday morning. You'll need to verify the St. Peter's situation separately, because the Museum calendar won't provide that information.
The basic admission tickets are listed first; they are 20 euros per person plus a 5-euro booking fee (I think also per person). Part of the way down the first page are the Vatican's own tours of the Vatican Museums and Sistine Chapel (combo tour) for individuals. Those cost an extra 20 euros per person. You'll be asked your language preference. For the random February date I chose, both English tours were already sold out, so if you're interested in a tour conducted by the Vatican (which will be cheaper than commercial alternatives), you should check immediately to see whether something is available for a date that works for you.
There are audio guides available for folks who want to tour on their own or can't book a tour because they're all sold out. I don't remember what the fee is for the audioguide, but it's considerably less than 20 euros.