A ten gallon tank is not big enough for three goldfish. They can reach around a foot long and can live for 20 odd years. The general rule seems to be 20 gallons for the first goldfish and then an additional 10 gallons for each one you add. A 5 gallon tank is fine for one goldfish for a few months whilst it is only tiny, but if you want it to live a long and healthy life it will need a lot of space. Unfortunately lots of places will sell you goldfish under the impression that they grow to the size of the tank, which just isn't the case. They will become stunted and then soon die, which is why most people will tell you that the average lifespan for a goldfish is something like 4 years... not true!
When I first got my fancies I was told all the wrong information and bought 2 teensy little baby goldfish (a veiltail and an oranda) and put them in a 5 gallon tank, thinking they wouldn't get too big. They grew VERY FAST and after some research I realised that they needed more space and now they live (with a third goldfish - a black moor) in a 30 x 12 x 20 inch tank. That's the bare minimum for them to be living in though to be honest.
So far as plants go, you'll want something that has nice tough leaves because goldfish like to nibble on plants (pesky things). I recommend amazon swords, java ferns, vallisneria and cryptocorynes... all of which should grow with moderate lighting and will withstand the occasional nibble.
If your goldfish is the one in your avatar it's very cute looking! Hopefully you'll enjoy keeping it for many years to come! And sorry if I sound preachy before... I don't mean to!
