The issue of structural integrity is quite important with a tank this large. Not to get off on a tangent, but most people forget that buildings are designed for and have specific limits. Only when porches come crashing down killing people do people realize that buildings are engineered for specific loads.
Lets do some quick math based on what you have said so far.
Tanks dry 600 pounds
Stand dry 300 pounds
500 gallons of water @ roughly 8 pounds per gallon is 4000 pounds
Equipment 250 pounds
So far thats
5,150 pounds
Just with this round number, you are looking at a tank that weighs more than
Would you park a ford F150 in your living room and not be concerned about the structure?
Its different when you consider it like that.
Also, consider that simply "reinforcing" the existing structure isn't always the right action. The load of the fish tank needs to transfer to the earth through various framing and structural systems in your home. The load will transfer like this.
Subfloor -> Floor joist -> Beam -> Column -> Footing
Along all of those paths of travel, the load has to be supported within the design limits of each component.
Certain efforts can be made to eliminate some of the considerations from the list. Putting the tank next to a foundation wall or on a concrete basement floor slab are some of the often used ideas for minimizing overloading any one element.
Long story kinda short. Yes, you need to consider structure. Most definitely.