You need to reseach 2 things, the type of fish you get (before you get them) and the nitrogen cycle. You tank didnt go through its cycle is why they died when they did, although some fish are hardy enough and used as fish to cycle the tank, many fish cant survive it. Species research and knowing what you're buying is even more important, the "sharks" you bought are probably either red-finned or red tailed sharks, which are the most common. They are both highly territorial and highly aggressive, especially towards its own kind or any fish that looks like a shark. One of them will, more then likely, establish its territory (which in a 20 gal would be pretty much the entire bottom of the tank) and kill the other. The most common "suckerfish" sold (and often recommended for beginners) is the common pleco, which gets over a foot long and needs to be in no smaller than a 75gallon tank. The "other fish" could have been anything so I cant help you there. I recommend you read a few articles online about setting up your first tank and read about some good beginner fish; heres some websites you should check out to get off on the right foot:
http://www.fishlore.com/Beginners.htm
http://badmanstropicalfish.com/2ndpage.html
http://www.theaquariumwiki.com/Category:Beginning_Fishkeeping
http://faq.thekrib.com/begin-cycling.html
http://www.firsttankguide.net/