Congrats! Which Tauck are you doing?
I'm pretty familiar with stalking flights since DD exchanged WDW for Europe at the age of 13 and hasn't looked back, lol.
United releases their award flights "about" 331-335 days out (depending on partner v. United flights and other random things). If you have a few minutes, I'd go and look at the flights you want as far out as you can...right now it's late Mar/early Apr to get a feel for the flight times, etc. Then I'd check back about every month or so-just to get an idea of the flights during the season you're flying --often they'll add more during high travel like summer/holidays. This will give you an idea of the number of miles you'll need and how much taxes will be (those vary by carriers and location).
Then, as the flights you actually want approach, I'd put it in the calendar with an alarm and start looking, very specifically, for the exact dates/flights you want, ensuring you have the number of miles you'll need for premium economy and/or business saver flights. If you're wanting to fly in late June then that means late July, you start looking-early August for the July 5th flight. Personally, I'd consider whether round trip makes more sense than 2 one- way flights--sometimes it's cheaper, sometimes not (now would be the time to play around with that!
). If you're doing "round trip" then another drawback is having to wait until the second date and you could lose your desired seats on the outbound trip so that is a consideration. I'd guess that 4 seats in the summer would be competitive so keep that in mind.
TL;DR-start stalking the website sooner than later to get an idea of when flights are released, which flights you want, and how many United miles you'll need in an ideal situation. United flights are often released or a different day than partner flights and economy flights are released usually a day or two before premium economy/business so you can get a "feel" for when the exactly flights and seat type are released by watching the patterns. Then definitely be ready-even if it's a day or two before you think it's time, to watch so you can see how/what they're releasing. I'm in the middle of this for our late April flights from Athens back to the US so I'm there almost daily, lol.
Also-remember that getting through customs and immigration and pulling your bags and rechecking them can take a while so definitely leave enough time for that on your flight home. Please pm me if you have any other questions.