As with most of the rides, the shortest wait times for hard-to-meet characters will be at the start of the day. Luckily for you, the classics generally are easier to meet than some of the princesses and other characters, so you shouldn't have to worry as much. Most of them are available in every park, too!
I'd suggest getting a FP+ for the Character Spot in Epcot - this will get you Minnie, Mickey, and Goofy in one go (separate photos, but one line). [Use your other Tier 2 pass in Epcot for Spaceship Earth - none of the others are worth it / need it.]
Pluto is easiest to meet at the front of the par basically any time in either Magic Kingdom (at the flag pole) or Epcot (behind and to the right of the fountain as you enter). Chip & Dale are easy to meet in Epcot (behind the Character Spot Building) or Animal Kingdom (usually outside the entrance during he park's first hour open or at Rafiki's Planet Watch the rest of the day), although they're at both other parks, too.
Hollywood Studios is where you'll find Mike and Sulley - way at the back beyond Toy Story Mania. Donald/Daisy/Goofy/Chip & Dale rotate at the Center Stage Courtyard wearing their "red carpet" attire. Minnie currently meets in the Disney Jr area near the Star Wars Launch Bay.
In Magic Kingsom, just at the baginning of the day, Minnie meets at the flag pole next to Pluto, with a separate line. (She's replaced by Marie a while after the park opens.) Minnie, Daisy, Goofy, and Donald also meet in circus outfits in MK in the New Fantasyland area, with one line for Minnie and Daisy and a separate one for Donald and Goofy.
You can meet Mickey at the front of Magic Kingdom in the Town Square Theater - he can actually talk to you here, but that line can be a little longer than others, so go early or in the evening for the best wait times. (Tinkerbell meets in the same building and has a great set, so I'd stop and see her, too, while you're in there.)
For nearly all the classic character meets, your wait will likely be 5-15 minutes, almost any time of day, *maybe* 20 or so for a couple of the busier ones.
As for general advice, I always find collecting autographs to be a great way to break the ice with characters when I'm solo. It gives you both a few moments to figure out fun ways to interact. Grab a sketchbook or even a ball cap or something and a good Sharpie, and then you'll end up with a great, inexpensive souvenir, too!
