I have never stayed at a value or moderate Disney resort, but did stay offsite very budget with my (now) DH the year before we got married (at a Residence Inn in Kissimmee, which is now some super cheap hotel). We did have a great fun vacation! It was his first one ever in his life.
I like having:
a balcony,
queen beds (not double) or a king
room service
a pool with a slide for my kids
and interior corridors.
I go frequently alone with my kids, and wouldn't feel so safe without interior corridors.
I need the balcony for my morning coffee, so I don't wake the kids. Now, I can and have done the go into the bathroom thing when they were younger, but I do like a balcony. Also, DH has asthma, so I have to have some fresh air.
I do not like being on the monorail (although we did love our stays at the GF), as the MK isn't our favorite theme park. We love Epcot, so really my ideal place to stay is the Swan and Dolphin (the pool is great, the service is good, and the price is very low) or the BWV (love having the space and the washer/dryer, and the location).
We usually order room service a few times, as sometimes we're tired late at night. I also love that at the Swan and Dolphin, you can order movies on demand. I wish Disney had better tv choices like that! It's not like we watch a ton of tv, but it's nice to have something either at night with some snack, or when they were younger to watch while I got us ready in the morning.