Your children are still quite young. Can they share a double bed?
If you do trips in the future, as they get older, then it will become harder to share a room with all four of you (we outgrew that comfortably years ago, but I have teen/young adult kids now).
When my kids were little, we would share a room.
Your first trip will be memorable no matter what! The kids will have so much fun at the parks that the theme of the resort won't make any difference to them one bit. It's more about what you're comfortable with.
After many stays at deluxe resorts, and the pricing going up so much, my daughter and I stayed at Pop Century last August and loved it! It was just great, and we also did a two night stay over spring break with my son along (then my husband joined us when we moved over to AKV Kidani). She and I shared the one double bed, and gave my son the other one.
I'd take a look at Pop Century just to compare. You don't really "need" the suite space, but I also agree the Little Mermaid rooms are far from everything and not worth it to me.
Have you also considered pricing out points rental (like from David's) to see if a one bedroom villa somewhere would be a good idea? Our first stay all 4 of us we were at the Boardwalk Villas in a one bedroom villa, and it was amazing. My kids were 2 and 4, and Epcot was their favorite park (still is), so walking to Epcot was terrific!
The biggest difference with a moderate is a pool slide (not sure how much that plays into it), a sit down restaurant (we hardly ever do sit down meals, but if so it's likely at a park), queen beds instead of double now that they replaced them all, and a coffee maker. I bring a coffee maker, daughter and I each get our own bed, so Pop is where we're returning end of August! I can't justify the high costs of other resorts any longer!