You may start with Livebearers. They are fish that give birth to fully-formed young fish. Egg-layers do just what their name says: they lay fish eggs that then have to hatch. Both types of babies (called “fry”), are somewhat vulnerable because they can and will be eaten by any other fully-grown fish in their tank, including their own parents.

I would recommend Black Molly or Black Tetron. They are perfect for starters and it's easily available in any aquarium shop. They are very easy to take care of too however be sure to study about them before trying to take care of them.

I have to ask why you are wanting to breed? A 2 to 5 gallon tank is barely adequate to keep a breeding trio of small live bearers and would quickly get into trouble once you had fry. The extra bioload and small volume with mean ammonia would be a constant problem and fry would have trouble escaping being eaten by the parents. If you breed for profit no store really wants common livebearers from an unknown source and certainly not as young fry when they are still likely to die off under store conditions. if you have a rare strain you could sell online but a 10g would really be your minimum to raise them, probably two tanks so you can separate fry from breeders.

First and foremost, I would suggest that the tank size that you are looking at starting out with is very small. How many fingerlings are you looking at starting out your breeding with? If you insist on that size of tank, then it's very important to keep the fish to a low number in the pond. I can recommend starting with either Black Molly, Live bearers or Black Tetron.

There are lots of breeds to start with but we all have our preferences when it comes to fishes to start with. My favorites happens to be Goldfish and Black Tetron. If you are starting out a new aquarium, just ensure that you have all the necessary conditions that would encourage their survival in place so that they don't die off.

I think breeding is really hard to in just simple aquarium. I have 8 goldfish and been two years now in my aquarium and even I saw their eggs, never see a baby goldfish coming out there.