If I could wave a magic wand and change things, here's what I would do:
1. Increase pay for senators by 10x, and for congresspeople by 5x.
2. Institute term limits, maximum of 4 consecutive terms.
3. After leaving office, total ban on direct employment of any kind for a period of time equal to the time spent in office. During this 'freeze' period, give them a pension equal to their pay while in office.
4. Strict limits on the nature of employment allowed for spouses/children/close relatives.
5. Strict limits on volunteer/nonprofit work, board positions, and anything else that isn't direct employment.
6. Lifetime ban on political lobbying.
7. Ban on any investing outside of a blind trust for the duration of their time in office plus the duration of the 'freeze'.
Overall, my thesis is that we should take away as much as possible of the opportunity and the incentive for corruption for the purpose of financial gain. We do that by paying officials gobs of money and preventing them from participating in the system outside of their defined role as a government official.