Hi mcdaniel. For the most part, you can keep the same assortment of aquatic plants in cold/temperate water tanks as you would most other fish tank setups. Most of the commonly available plants we keep are well suited for a vast range in temperature. As always, if you're not sure about a particular species be sure you check into plant profiles and care requirements just to be sure.
It wouldn't be very practical for me to attempt making an all-inclusive list of every possible plant variety that will do well in a goldfish tank. There are just too many of them to even try to list ALL of them together. I can give you some helpful information about a large number of common aquatic plants that would serve as a great start for you. Beyond this, you could expand the selection even further if you'd like and experiment with new varieties on your own.
A planted tank offers many advantages for keeping goldfish, in particular. Plants consume ammonia, nitrite, and nitrate and they become part of the biofiltration in your tank. Healthy growing plants also produce oxygen for the fish - and they feed off of excess nutrients produced by fish waste... thus, helping to keep the water quality high.
Your best bet starting out would be the more rugged, easy to grow plants. Your goldfish are going to nibble and graze on some of them, so don't use anything rare, expensive, temperamental, or particularly delicate. That would be wasting your money. Safer choices would be anubias (big and small), java ferns, most crypts, larger sags, dwarf onions and other crinums, anacharis, hornwort, bolbitus, sword plants, moss balls, and some mosses.. along with your choice of floaters (if you want any of those), such as duckweed, Amazon frogbit, or water lettuce.. even some water wisteria. This assortment would make a nice start and they let you maintain a beautiful aquascape that's heavily planted and will fare well having goldfish in there. Once the plants you start with from those get established, then you can add more delicate plants here and there to add more interest (if you want)... such as aponogetons, dwarf lilies, barclayas, and hygros. Or, really, anything else you're willing to experiment with. These plants all have more tender leaves, but even if they get nibbled on.. they also grow new replacement leaves quite fast.
Generally, you should avoid the super bright light plant species that would need higher levels of CO2. Goldfish need a lot of oxygenation so we we'll usually provide them with an air pump and bubble wand for this reason. They also love to play in those bubbles. This, of course, makes CO2 injection highly impractical for a goldfish tank because any CO2 you pump in there would just gas off right away.
Until your plants have well established root systems (or rhizomes attached to rocks/driftwood), it would help to place a few stones around them. Goldfish are always exploring the bottom in search for more food. (This is how plants often get uprooted in the beginning.) This is also your main consideration for substrate type. Goldfish commonly root around, taking up mouthfuls of sand/gravel and spitting it back out. Larger pieces of gravel can become lodged in the back of their mouths.