Hi again Edd,
Josh has got you covered there with OM47's link to Miss Wiggles thorough article.
It never hurts to hear it several ways though, so I'll ramble on a bit. To answer your question again, its just as Josh said, once the filter is cycled, it should/will maintain ammonia and nitrite(NO2) levels that test as "zero" with your test kit. The nitrate(NO3) level will be somewhat higher than your tap water because the NO3 is what is finally produced as the end-product of what these bacteria do when they process your ammonia and nitrite(NO2.)
In your case (at least initially, since sometimes it takes beginners a while to get the hang of good testing technique) it appears that you've got some ammonia and NO3 in your tap water (must live in the UK? or Chicago, LOL) and I'd suggest you re-test your tap water occasionally (prior to a water change maybe once a week the next few weeks would be good) to see if these excess levels hold up in the tap water. The nitrate(NO3) test is notorious for being difficult to perform (especially for the impatient) as it requires some extreme "shaking" times and even those are basically minimums, so use a timer and get them right.
OK, so what you'll be getting out of the "fish-in cycling" parts of the linked article should be something like this: Your main goal in fish-in cycling is to be a detective of sorts. Your tools are your test kit and your ability to do water changes. What you want to accomplish is keeping ammonia and nitrite(NO2) close to zero, having it only rise to a max of 0.25ppm (yes, both of them, ammonia and nitrite) at which point you magically appear and do another water change for your fish. You're trying to figure out a pattern of water changes and you can vary both the percentage of water changed and the frequency of changes. In your case, you may never be able to get below 0.25ppm because of your tap water, so for you it will have to vary between 0.25 and 0.50ppm assuming that tap measurement holds up. Nitrates(NO3) by the way are not something to seriously worry about for now, so just test them occasionally and note the results in your logbook.
Its not, of course, as hard as all these words make it sound. You will soon see that perhaps one 50% change per day will work, or maybe two for a while, then dropping to one or something like that, maybe even less will do the trick. The point is, you yourself will become a reliable biological filter (poison diluter!) for your fish during this next month or so, keeping their water as fresh as is possible, given your slightly polluted tap water. (By the way, we're talking parts per million here, so its not at all harmful for humans, its just fish are more sensitive than us.)
Meanwhile, the very fact that there is ammonia (regardless of how small the amount) in the water and that the filter is plugged in and moving water through the filter media is going to be providing a great environment for these 2 species of beneficial bacteria you are growing. What they like is food (ammonia) to eat and fresh oxygen (the water flow provides that) and some good surfaces to grow on (your sponges, ceramics, whatever biomedia you have in the filter, provide that) and they will be (slowly) multiplying and making your filter look brown and stained inside (yes, that brown muck is good!)
Let's be sure about your water change technique: You need to use a gravel-cleaner type siphon. It usually has a large clear cylinder that you shuffle into the gravel, to allow the gravel to churn up and the debris in that patch to be pulled up with the water that is draining out of the tank. This clears some of the excess fish waste, excess food and plant debris that are always starting to build up in an aquarium. The siphon can drain out a window or door to a garden or to a bucket or to a drain. Stop at halfway (50%) or whatever you've planned. For the new water you will need to be safe (a good approach I think for beginning cyclers because by definition their bacterial colonies are not robust) by conditioning and temperature matching. Conditioning means following directions on a dechlorination/dechloramination product (Seachem Prime is widely regarded as one of the very best, but almost all are fine) and dosing it as they say or 1.5 times or even 2 times what they say, but not more than 2 times what they say, ok? Temperature matching means the return water should just be roughly matched via your hand so that the incoming new water and the tank water feel pretty close to the same. You can either use buckets (conditioner by the way works instantly) or you can dose conditioner directly in the tank and use a "Python" type hose to fill the tank directly from a temperature mixing tap (in USA we have glass-lined hot water holders, so there is lower worry about excess metals, but many in UK worry about this if their boilers are involved and they heat kettle water.)
Finally, how do you know how long to do all this water changing? Well, eventually (usually one can expect around a month later) you will notice that you don't think either ammonia or nitrite(NO2) are creeping up on you when you come back to test. So you try not doing a water change (and test maybe 12 hours later).. and you keep doing more of this and finally when you find you can go two full days with no water change but your ammonia and nitrite are now staying at zero (by now your bacteria will be eating even all of the ammonia coming from your tap too) then you are essentially cycled. Just keep testing intensively for a week or two to be sure and then ease down on your rate of testing. By the way, all the while during fish-in cycling your fish should be behaving pretty happily (good colors and perky behaviours) because you are now monitoring and providing the nice fresh water they need and want!
(ok, well I rambled on as long as MW does in her article, so I guess we can just hope this will sit out here for you as a little extra reference material, LOL)
~~waterdrop~~
and unfortunately I am going to have to hang on to the fish whilst i/we get this sorted. I woke up nice and early and did the water tests (I felt like a chemist)
Also, ignore any and all instructions to replace the catriges and foams regularly, thats just the manufacturer after your hard earned £...
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