I'm doing a similar trip in late August. We will taking the High trail from Agnew to TI, over Donohue on day 2, and then out @ Toulumne on the last day. (We will return to Mammoth via YARTS.)
I like the area for its quick access and easy hiking. It's a great place to introduce new hikers, since it's one of the most beautiful areas, combined with perhaps the easiest hiking in the high Sierra.
As for choice of trails, I prefer the High trail, but only if you get an early start. The first shuttle arrives at stop 1 (Agnew) around 7:45am (leaving MMI @ 7:30am). Summit lake is 6 miles away, so you need enough water to make it that far.
I take 40oz on my straps (two 20oz Gatorade bottles) + a 1L Platypus in my pack. Once you make it to Summit, the Plat can be folded up and stored away.
The High trail has by far and away the best views, but if you get going after 11am, you may be too hot to admire them. If you start @ 8am, you can reach Summit within 3 hours only going 2mph.
Here's a view of Banner/Ritter from Summit:
If you are getting a late and/or afternoon start, then definitely take the River/Shadow/JMT trail. You don't want to to be on the High trail in the afternoon, unless you like walking around in Death Valley. Finally, if you like to hike in the very late afternoon and arrive @ dusk/evening, you could start around 6pm & stay overnight @ Summit.