I actually have a few ideas for what time periods to go back to:
1. You mentioned that a lot of the buyers would use the machine to gain profit. A very profitable point in history would be the Prohibition era in America from 1920 to 1933. The user could bring alcohol back from the future and sell it in the 20s for a large price or they could use future knowledge to make or gain alcohol quickly and sell it to the right people. (The labels of bottles from the present would be torn off, so the person drinking it would be none the wiser that the bottle is from the future.)
2. Maybe one of the machines was sold to someone who hates America. The machine could have been sold to someone who hasn't let go of the cold war or someone from the Taliban or North Korea. They could go back in time and try to turn the tide of the revolutionary war in the British's favor.
3. A more original idea in my opinion, is that the IRA (Irish Republican Army) bought one to go back to the Irish war of independence (1919-1922) and beat the British.
4. An idea that I like is where an escaped serial killer managed to get himself one of the machines and hide in the past. He hides in Victorian London and the big twist would be that the escaped convict from the future turns out to become Jack the Ripper.
5. A final idea that is a more personal one. A woman has managed to buy a time machine on the black market. Her parents were killed when she was just a small child and she ended up living in a horrible orphanage with no one to love her. She is so distraught and stuck in the past about why her parents had to die. For reasons that will be explained, she found a time machine on the black market and bought one. She goes back in time to prevent her parents death. Her parents died in a car crash after a school bus nearly swerved out of control and hit them. This caused the car to swerve out of the way and crash. If the parents were prevented from going to work then they would live but the bus that swerved would swerve in the wrong way and would crash into the side of a building, bursting into flames. All the children would die. The event was 40 years before (She is 45) and one of the children on the bus would become someone who invented a cure for H1N1 (or any other disease). Since that person is now dead, they would not be able to prevent an outbreak that happens a couple of years before the present and it would cause the death of 10% of the earth's population. Her intentions were good but the need of many versus the need of a few.
This is just a small set of idea, feel free to use them, tweak them or not use them at all. Your choice. :)