Well, by tank conditions you mean parameters, here's what should be followed:
0 ppm ammonia
0 ppm nitrite
less than 20 or 30 ppm nitrate
I personally keep to less than 20 for the nitrate.
If you're unsure how to test for water, you can purchase a water testing kit at your local petstore or if you know a petstore that specializes in fish, you can ask them to test a sample of your water for you. We recommend that you purchase a kit yourself and read the intructions so that you can do the tests on your own -- you'll be testing your water a LOT!
You may want to take a look at this link:
http://www.kokosgoldfish.com/cycle.htmlThis will explain how to "establish" a tank -- this basically means creating a tiny ecosystem that helps remove waste and other byproducts.
And of course, when picking a filter, choose one that's rated 10x GPH for your tank. So for example, if you have a 10 gallon tank, you'll want a filter that's rated 100 GPH. I recommend choosing a "hang on back" powerfilter since they tend to include more spaces to promote biological filtering.
Good luck on your tank and don't be afraid to ask more questions!