Welcome to the DIS! Your questions are not dumb at all. And I'm going to chime in on them - in reverse order - with a really long-winded response.
Counter service is plentiful at all parks and most resort areas. There are many places that serve the standard burger/chicken strips, but there are some stand outs in my mind also. At MK, the Main Street Bakeshop does some nice breakfast items (including some hot items), Columbia Harbor House in Liberty Square has great soups and sandwiches (though you can still get chicken strips), and Cosmic Ray's in Tomorrowland has some very tasty chicken. At Epcot, the World Showcase area counter service places offer the cuisine of the country you're in ... Mexican, Chinese, French, etc. I'd recommend Norway for sandwiches, China for potstickers, France for just about everything, and the UK for fish and chips. Nothing really stands out at me at MGM or AK, but there are certainly a number of choices available. If you don't like a menu, keep walking until you find one you do (i.e. at AK you can get pizza or barbecue depending on where you go). At the Resorts, there are standard choices and some specialty items, like Tonga Toast (stuffed french toast that may lead to a sugar coma) at the Poly or beignets (donuts that will definitely lead to a sugar coma) at Port Orleans French Quarter. You might want to glance at the menus for your resort or the ones around you if you intend to eat there much -- which may well be the case if your little ones will need naps/breaks at the resort. If you happen to be staying in the Epcot area, Beaches and Cream at the Beach Club is a fun place to grab a burger and some ice cream.
Character dining is fun. Only certain restaurants offer character meals, but, if you're in the restaurant, you're having a character dining experience. There isn't an add-on or a choice you have to make in advance - no areas of the restaurant are left out. So, if you go to Crystal Palace for breakfast for instance, Winnie the Pooh will come over and say hello to you and everyone else who happens to be eating there. Character meals are part of the dining plan. I believe they are all just a standard 1-credit meal with the notable exception being the Cinderella character meal inside Cinderella's Castle at the Magic Kingdom. Since you have boys (and a daughter who is probably too young to notice), I'm guessing you're going to want to skip the princess meals anyhow.
Before I list some restaurant ideas, I'll add that even with park hoppers, you probably don't want to do much travelling just to get to a restaurant. I'd suggest looking at the park hours, determine where you might think you'll be on the days of your trip, and then making dining reservations that correspond with that schedule. Also, remember that you can cancel and change dining reservations. (Make the ones you think you want, and, when you get there, if it's not going to work out, just cancel or adjust them. Having reservations is pretty much a must to make sure you can use all those dining plan credits, though.)
Ok ... some ideas for table service meals given the ages of your kids and not knowing where you're staying ... and keeping in mind that all the menus are available for you on this site...
MK: Crystal Palace offers meals with Pooh and his friends. It's a buffet and very tasty. I like breakfast best, but lunch and dinner are good, too. You can also have a family style meal with Mickey and his pals at Liberty Tree Tavern. There are mixed reviews on the food here (Stouffer's products), but the character interaction is very good. For sandwiches/salads/burgers, the Plaza Restaurant on Main Street is one of my favorite sit down places. No characters. However, it's small, so it would be tricky with a stroller. (It's also not very pricey by Disney standards, so it's a nice place if you're paying out of pocket for a meal.)
Epcot: The Garden Grille offers character dining at lunch and dinner. Not one of my favorites, but worth taking a look at the menu. With kids, some of the the World Showcase sit-down restaurants might be overwhelming, but they are definitely welcome there. I think the atmosphere in the San Angel Inn (Mexico) would be fun for them and Rose and Crown (UK) does well with kids. Really, almost all of the restaurants at WS might work depending on your kids' eating habits. The only character dining is at Akershus in Norway, but it's a princess meal.
MGM/Disney Studios: There is a character meal with the characters from Playhouse Disney at Hollywood and Vine. It's cute and the food was good. Also at MGM, the 50s Prime Time Diner (mom as a waitress, tvs at the tables, 50s decor) is fun for kids. The Sci Fi Dine-In Theater lets you sit at a table that looks like a car and watch old sci fi movies while eating. Might be overwhelming for the baby, though. Also at MGM, there is Mama Melrose, which is casual Italian. Brown Derby would be very fancy and not a lot of fun from a little one's perspective, I'm guessing. (My niece is 4 and she handled it, but didn't particularly like it.)
Animal Kingdom: Donald's Safari Breakfast should be up and running at the Tusker House by the time of your trip. Might be fun for boys. The only other sit down dining here is the Rain Forest Cafe.
Resorts: Here's where the dining choices become overwhelming. There are character meals at Chef Mickey's (Mickey and friends) buffet at the Contemporary for b/l/d. I like this one, and little kids love watching the monorail go by over their heads. Very convenient from the MK, even if you're not staying at the Contemporary. The Polynesian has Lilo and Stitch (and Mickey and usually one other character) at breakfast at Ohana. I love the breakfast here and Stitch is my favorite. It's served family style, which may be easier than a buffet with the kids. The Wilderness Lodge also offers family style meals at the Whispering Canyon Cafe. We like it here, and it would be fun for boys with the wild west theme. No characters, other than the wait staff, but an easy boat ride from MK. Fort Wilderness also has a great buffet at the Trail's End Restaurant. No characters. Very nice if you're in that area. At the Beach Club, Cape May Cafe has a great buffet character meal at b/l/d. The other sit down restuarants in the general area (Beach Club/Boardwalk) may not appeal to kids very much, but Cape May is great. The Animal Kingdom Lodge is worth a visit with kids. There's great viewing areas to see the animals, and the buffet at Boma is great. The breakfast buffet is fairly traditional if the kids aren't adventurous eaters and you still want to visit. It's a nice stop on the way to AK if you have time. The moderate resorts also have sit down meal choices, but I can't say they'd be worth travelling to unless you were staying at that resort. No characters at those choices.
Downtown Disney has some nicer sit-down places, but I can't think of any that scream 'kids' to me. Certainly doable, but no characters or particularly great kid options. There are counter service options (and a McDonalds) here.
There are also several dinner shows available on property. They use more than one credit on the plan and, in my opinion, are not worth your time on your first trip when there's so much to see!
So, pick your parks, think about your resort location, and then call the dining people! Sorry about the really long response. Can you tell I like food?
Also, is there a big difference in counter service places, or do they basically serve the same stuff? Sorry if these questions are dumb to those with WDW experience!
