That isn't really long enough for it to be cycled I think. It really depends what you did. But if all you did was add water and the plants and let it run for a week it probably is not done.
I actually don't know how exactly to cycle a fish tank since when I set mine up I was younger and I didn't think about it (and ended up with a lot of dead fish!) but it eventually got cycled... And my other tank I've stemmed off of water/gravel/filter material from my established tanks already so no clue how to cycle a tank w/o any material from an established tank or anything like that... buttt look on google for some fishless cycling guides. As someone asked above if you had a nitrate/nitrite/ammonia tester I believe you will need that for cycling.
Fishless cycling is the more humane thing to do... what I unintentionally did when I was younger and didn't know about cycling and set up my tanks, was basically cycling with fish... and gave me lots of dead fish... so I reccommend researching fishless cycling so you don't have to harm any fish or stress them. :(
You can get
Goldfish, but
Goldfish get BIG so you will only be able to keep 1. Many people wouldn't recommend keeping
Goldfish in a tank smaller than 20 gallons.... some bright, pretty fish that are good for beginners would be many of the livebearers... and if you enjoy having baby fishies. (: Platies, Mollies, and guppies are beautiful fish, don't get too big, and are hardier than a lot of other fish. You could probably keep 3-4 of them in your 10 gallon tank and they'll be happy. :)
With a first fish tank it is hard to keep to a small amount of fish (because you just keep wanting to get more xD), but if you over crowd your tank your fish are going to be unhappy and continuously die...
Nitrite, Nitrate, and Ammonia will be an issue even with a 20 gallon filter in an uncycled tank if you add fish. You see, it takes weeks for a good bacteria colony to establish itself in your fish tank. This bacteria breaks down Ammonia into Nitrite into Nitrate (i think...)(Nitrates being the least toxic to your fish)If you don't have these good bacteria established in your fish tank, your fish waste (ammonia) will spike since the bacteria won't be there to change it into less harmful chemicals.
And nitrate can still be an issue with a cycled tank! Even if you have a filter which can handle 2x the ammount of water. If you don't do regular partial water changes the nitrates will build up in your tank and become poisonous to your fish! Water changes are very important, don't rely on your filter to keep your tank clean, it can't do it by itself!
70-80 degrees will be an ideal temperature for most tropical fish. Check your potential fish's stats online to see what temperatures they like.