How to build MtG duel decks out of a set of older cards?
It appears that what you have is actually two 60 card decks already, plus a few extra cards. 

Make a Blue deck and a Black/Red deck with 24 lands and 36 spells in each using your existing cards. In the B/R deck make sure to split your colors in the same ratio as your lands are divided. In both decks try to have at least 2/3 of your spells be creatures.
I didn't take a close look at your cards to see if there are any synergies or obviously good/bad cards.

Following the above guidelines should get you to a good starting point for the decks. Play them a 5-10 times and then consider if there were any cards that were either far too good (you always win when you resolve it), too bad (you never wanted to cast it), or unfun (maybe Capsize later in the game). Take those cards out and replace them with ones that are more interesting.

After you've done that for a few play sessions then you might consider actually buying cards, either by increasing the count of the cards you like best to 4 (the limit), or by finding a theme or strategy that you like and moving the deck in that direction by cutting cards that don't fit and adding some that do. Searching the internet for "mtg {cardname} combo" or "mtg {cardname} deck" will often yield results that will give you some specific cards to look at. It appears to me that perhaps you are asking how to do this step, and really the answer is that you have to play the decks to find out what you like or don't like about them- there are thousands of cards that could be added to each deck, and each one will take it in a different direction. The one person who is qualified to determine what you like or don't about your decks is you.

Once you have selected some cards that you'd like to buy, you can find them lots of places online simply by searching for "buy mtg {cardname}". Do compare prices of the cards and shipping- online stores often have wildly different prices. Retalier aggregators like TCGPlayer can be useful in this regard.