You think your head is spinning, try researching a reef tank
I had mine for 3 years and I still don't know half of what I should have!
The digital ones are always best, but you can use a floating one too. The stick on ones aren't good since they also read the air temperature and you don't get that accurate of a reading. The heater depends, really. Some fish(like neon tetras or celestial pearl danios) come from areas where the water is cooler and get stressed out in warmer water, definitely wouldn't need a heater for them. Others, like bettas and I think guppies come from warmer waters and get sluggish and sickly without them.
www.fishbase.org will tell you the temperature that the fish you are looking at would encounter in their native habitats and you can go from there. If you have a cooler water fish and your tank always stays at a constant temperature, you don't absolutely have to have one other than for peace of mind. If you have warmer water fish or your tank's temperature tends to swing a couple of degrees from the lights or air conditioning you definitely do. I don't think any of the big market filters have heaters in them. I think I've read about some high dollar ones for reef tanks and the like, but that was ages ago.
As for pumps, I'd assume you mean the air pumps that make bubbles in the tank? I've had them but they don't really do a whole lot in for a normal run-of-the-mill tank. If you aren't running a filter(like for a smaller betta tank) you can use them for water movement, or if you've got goldfish who need better oxygenated water they're great, and some of the little knick-knack type of ornaments run off of them. And the bubbles look nifty sometimes, but unless you want one there's no real reason you need them.
ALSO! I can't believe no one(including myself. Bad self.) has mentioned this! Stay away from a fish unless you know it is NOT dyed. Petco and Petsmart don't sell ANY dyed fish, but a lot of local stores and wal-mart(if you have one that still has fish) and some smaller chains do. Basically they take a fish that is supposed to be(most of the time) white, strip its slime coat off with acid and drop it into dye to make its colour different. It's entirely cruel and kills the fish essentially. Most of the ones they do it to end up pink or blue and get called random things like "gumdrop" or "jelly bean" or "painted" instead of the regular species name. Not a whole lot have it done anymore, but something to be cautious of for sure.
. Thanks for the advice Carole. So, Goldfish need a bigger tank, filter, pump, sounds like they need a lot of equipment to me, but do they?
