If you want the cows to calve together, then synchronization isn't a bad idea. For three head, I would just use Lutalyse and see how things went. That's the most simple and least expensive, and the benefit of syncing three isn't like the benefit you would realize from having 30 grouped together.
Obviously, we don't always know what day of the cycle a cow is on, but yes...Day 0 is standing heat. The next day is day 1... Textbook is 18-24 days with the average being 21, but my experience has been most will be 18-21 days. We occasionally have one go 24 days but not very often. When you get ready to breed, heat detection is very important. AI about 12 hours after the onset of standing heat. If you'll watch them for 15-20 minutes at least twice a day (morning & night), and assuming they show normal heat, you'll see when they're standing and should be able to guess about when they started. Good rule of thumb if you don't know exactly: If they're standing at the a.m. check, breed that evening. If they're standing at the p.m. check, breed the next morning.
I'm curious why you want to wait until June/July to breed these females. There aren't a lot of convincing arguments for late spring calves where I'm from. And I'll tell you this...the hotter the days when you're trying to breed, the more difficult it can be to catch them in heat. It can be very frustrating. If you're set on summer breeding, you'll wanna plan to check for heat early in the morning for best results...like 5-6 a.m.