Do you mean entry tickets? Buying tickets from anywhere other than the official ticket website will cost you a substantial premium. I rarely take tours, but others enjoy them a lot and find them totally worth the additional cost.
A couple sights in Rome are proving to be massive problems even now: the Colosseum/Forum and the Vatican Museums. Scroll back through the list of most recent threads on this forum and you'll find the latest news. Cutting to the chase, you'll probably need to get up in the wee hours of the morning on exactly the right day and cross all fingers and toes to get regular tickets to those places.
The Vatican Museums are massively overcrowded. For a better viewing experience, you can consider signing up for one of the early-access tours that get you into the Museums before the public opening time. They do cost more, but they may well be worth it to you. The July tours have probably been bookable for some time, so you can check now to see whether your dates are still available on the Vatican Museum website. There are private companies offering similar early-access tours, but they cost somewhat more than the Vatican's offerings. Vatican Museum ticket website
CoopCulture website for Colosseum/Forum tickets
The Borghese Gallery doesn't necessarily always sell out months in advance, but it requires prebooking. A friend of mine will be in Rome April 27 - May 3 and was unable to get tickets during that period. I really don't know how early you'd need to buy for July. This might be another place where you'd need to buy the tickets the minute they go on sale in the middle of the night US time. TicketOne website for Galleria Borghese tickets
The Domus Aurea is open only Friday-Sunday, and it sells out in advance. CoopCulture handles the tickets for the Domus Aurea, but I can't seem to find a current link. All visits are by tour. This is a working archaeological site, so you can't wander around freely. (Take an extra layer of clothing; it will probably be chilly.)
Those are the problem sights I'm aware of; others may be able to contribute to the list. The other places I went in Rome were no problem, but I was there in February and March. July is an entirely different situation, and you might encounter ticket lines where I just walked right in.