I play Flower Town on my red 3ds and I haven't bought pots in some time. I use the pot that you can use unlimitedly, but does that pot affect the color of my plants, the plant breed( does it increase the percent of a new breed?), or the plant's seeds?
No, The pot is purely a decorative piece meant to make your gardens look different - it has no bearing on the plant's colour or breed.
The colour and breed comes from the seed itself - when viewing the seed box you can see what the plant will potentially grow into. The higher the percentage chance, the more likely it is you will get that variation.
Remember you can always change the pot that your plant is currently in at any time, if say you earn some money and want to splurge on some nicer pots.