You should be safe with perennials around the tank, but no trees or shrubs. More importantly, where does the sewage go after the tank? If there is some kind of absorbtion field on the property, that would be the bigger concern as far as planting. Tree and shrub roots getting into the absorbtion area can cause major damage to an on-site septic system.
I am currently purchasing a property where tree roots have caused the complete failure of a seepage pit system. The closest tree (silver maple) is 20 feet from 1 of 3 seepage pits.
How about an annual bed? Annuals are great for what you are doing. You could go with a nice mixed bed of petunias, marigolds geraniums maybe for some added height in the rear you could use snapdragons. A medium size stone located between the tank covers would add some character to the bed. Don't worry about weight on the tank with the stone. Those tanks have six inch reinforced tops. You won't break the tank.
Septic tanks are not a big problem. All you need is access to the lid to empty it. If the lid is deep, you can add a riser to bring it close to or up to the surface. Roots entering a tank is not much of a problem, as someone else mentioned it is the soil absorption component that has that problem.
The problem here is access. If the lid is deep it requires a big wide hole. That means moving several plants or having a big open area. Put the riser on the tank and maybe a nice stone or sculpture on the lid. Then you have no digging, you know where it is, and the garden will look nice.
PS. I am very involved with onsite sewage disposal system design.