Without more info on budget, general useage etc. most answers might be largely irrelevant.
Having said that, we have a Honda FR-V which is a 6 seater - 05/06 year can be had easily for under 5K - great reliability.
We find it great as 90% of the time we just need 3 kids in back, and one or both of us parents in front.
But if Nana and Granddad are visiting, they can be collected etc. without moving the 3 child seats. Most 7 seaters won't work as easily for this, in terms of gwetting access to the back row, and in our case Nana and Grandada are not mobile enough to scramble into rear row of seats of most 7 seaters.
Many 7 seaters also have very small boot space if all seats are in use - Honda doesn't have this issue.
Sounds like you might be asking about sticking to regular saloon car though, in which case you have to try the few mentioned in posts already, and bring your car seats along when you do. Most are a tight squeeze though, and a bit impractical day-to-day with 3 kids.
7 seater options - best to take a loo k at Ford-S-Max (New Grand C-Max if looking at newer), Picasso, Mazda-5 - etc.