AQUARIUM:
Start with as large an aquarium as you can afford. There is a very BASIC rule of thumb (this only applies to beginners), that is to have 1 inch of narrow bodied fish per filtered aquarium gallon. Goldfish are dirty and fatter, so I would triple this with them. Remember, many fish purchased can grow much larger than your original purchase size (ex: goldfish), so keep this in mind too.

FILTERS:
I always recommend two filters minimum per aquarium for redundancy and for improved biological (denitrifying) filtration. For a small aquarium, a combination of a hang on the back filter and a sponge filter. Or a sponge filter and an internal power filter. You want to make sure and rinse your sponge or cartridge out in used aquarium water to maintain your beneficial bacteria for bio filtration. Other filters of note include canister, wet/dry, under gravel, and fluidized bed.

HEATER:
Most tropical fish do well at a temperature between 76 and 80 degrees Fahrenheit. (Discus prefer warmer). Goldfish do not need a heater.

CYCLING:
Your aquarium will not be at peak biological filtration for 6 weeks (or more). To start your biological filtration, there are many cycling products available, such Cycle by Hagen. I prefer to add gravel or a used filter sponge/ cartridge from another aquarium. You can also just set up your aquarium and run the filters for a couple of weeks (pretty boring though, and this is also a slow way to develop aerobic bacteria). Cycling is what is referred to as the Nitrogen cycle. Waste (nitrogenous) from the fish is broken down first from ammonia (NH3, the most toxic) to nitrites (NO2, less toxic) to nitrates (NO3, least toxic- but high amounts can stunt fish growth and lower disease resistance).

FEEDING:
I recommend feeding high quality fish and plant based foods. Quality ingredients include: spirulina, fish meal, FD Brine Shrimp, shrimp meal, Vitamin C & E, lobster shell. Fish cannot digest proteins from beef well, and fish get most their energy requirements from fats. Some quality foods include: Omega, Spirulina 20, Ocean Nutrition, Hikari, Sanyu. Feed you fish two to three times per day what they will consume in three minutes. Feeding foods high in poor quality proteins can increase your nitrate levels, as an essential ingredient in protein is nitrogen, and if unusable by the fish, it is excreted, entering into the nitrogen cycle.

CLEANING:
You should try and have a schedule of changing 20% (or more) of your water every week. I recommend using a gravel vacuum, you need not remove the fish while using a gravel vacuum. Make sure the water you add back in is the same temperature and ph, and has no chlorine or chloramines.

CHEMISTRY:
Keep your ammonia level at 0, your nitrite at 0, your nitrates below 20-30, and your KH above 80 ppm. Ph depends very much on the fish you are keeping. Discus prefer under a ph below 7.0, while Mbuna African cichlids prefer above 8.0 A very general ph of 7.2 -7.5 works for many community fish.

CONCLUSION:
This is only very general information, there is much more in depth articles about each of these subjects and more available. A good reference point is Aquarium Information