Handheld ones with the motorised brush are great for fluffing up the carpet while maintaining great manoeuvrability and without lugging a heavy weight beind you.
In this case the Dyson v7 or greater will work well if it is a small / medium house.
I disagree with cordless Dysons. We have the V8 Animal and it's pretty pathetic. It struggles to pick up anything denser than dust and the very smallest of crumbs, and the battery life isn't enough to do a full clean of a house in one go. Most of the time we have to get out the old corded one to finish what the cordless couldn't. I think brands like Shark and Vax are supposed to be better but I've not tried them.