I'd suggest shrinking the pool somewhat, perhaps by selecting from people involved in state-level politics already? This idea that any random person is fit to be a representative is bonkers to me.
The House should be filled with the Common Man, if you will, but I'm certain the authors were envisioning a parvenu bootstrapper like Ben Franklin or a Paul Revere.
But the Senate should change too--repeal the 17th amendment and bring the election of US Senators back to the state legislative bodies. It's a key element that made us a Republic and I'm failing to see how we can even refer to ourselves as such since 1913. I find it grating when people say "our democracy" because it is true now, but shouldn't be.