When you pick your 3 choices, the system will give you 3-4 different options on the times you want. When you choose the option, if you don't like a certain time, you can go into each individually and change it to another time.
They seem to give you a good amount of time between FP+ times.
For example, on my Hollywood Studios day, I got Toy Story Mania at 4:05-5:05, Disney Junior Live at 5:20-5:35 and Voyage of the Little Mermaid at 6:10-6:20. If you get to the attraction at the start of your FP+ window I think you'd be ok.
Animal Kingdom day I have Finding Nemo at 10:30-10:50, Meet Disney Pals at 12:10-1:10 and the Safari at 1:40-2:40.
Magic Kingdom I had Dumbo at 2:05-3:05, Winnie the Pooh 4:05-5:05 and Meet Mickey at Towne Square 7:55-8:55. I didn't want the Meet Mickey that late, so I ended up changing it to 11:05-12:05. Then decided to change Winnie to meeting Cinderella and chose the Cinderella meet to 3:55-4:55.
Epcot day is Turtle Talk with Crush 3:00-4:00, The Seas with Nemo 4:00-5:00 and Meet Disney Pals 5:15-6:15.
BTW, we have small kids, so we don't have the most popular rides in the park, but I didn't have any trouble getting TSM.