2 Goldfish, 10g Aquarium Kit, General Care Questions?

Hi All,
I’m on my 3rd day of owning 2 small goldfish (1 comet and 1 fantail). Went through the fishless cycle for about a week and fish are doing well.
On this 3rd day, did the 4 tests (pH, Ammonia, Nitrite and Nitrate) and they were a little high. Water is slightly hazy. Did a 10% change as the kit advised, will test and check again tomorrow.
Thinking I should invest in a 20 gallon filter to help keep things in check. I understand that changing the filter after only a week isn’t a good idea. Should I then get one in a month’s time, when I think the cartridge is scheduled to be changed? A 20g tank is not really much of an option due to my own living space restrictions.
Another thing I am interested in is introducing live plants to assist in the filtration process (poop). Have plenty of artificials for comfortable sleeping spaces. Are live plants a good way to go for this purpose? Saw in the pet store “free snail included.” Why would I want this? Give the snail back?
I understand that goldfish are “high maintenance” and accept such responsibility. So any advice can help.