I agree with Daddy-o. Much of the tanks filtration comes from the rock in the tank itself. If you stock the tank lightly, you could get away without any hang on equipment or sump. You would be limited to not being able to do things like run activated carbon, UV, skimmer, fuge...etc. but you can be sucessful without. Most of that equipment just lets us put more fish into a tank.
Lighting for a simple reef tank would likely be your biggest upfront cost. Depending on what coral you wanted, 2-4 of the black box lights would do it, so $200-400 in lighting would be the minimum expected and up from there.
People often add equipment in order to try to fight off algae and such. Being limited on filtration may mean more manual labor on your part picking out algae if you have an outbreak. It's an addicting hobby for sure, but can be a done on somewhat of a budget if you go into it anticipating that and working around it.