[RogueRose]

It seems that H2 is one of the most commonly produced gases from chemical reactions followed closely by Cl2 (admittedly this is from my limited humble experience with chemistry).  Is there way to capture either of these two for later use?  I'm especially interested in H2 if it is possible to compress it into something like a small propane cylinder to later be used for tourch fuel. 

[Arkcon]

Uhh ...  Yikes.  That's what comes to mind.  Hydrogen isn't a typical fuel like methane, or paper.  At certain proportions with oxygen, it can explode.  You might want to look up other processes.  And see how these things are done industrially.

[Intanjir]

It is very unlikely that an individual would be producing enough hydrogen gas to do anything useful with.

In any case, you don't want to mess around with compressed hydrogen gas in an amateur capacity. H₂ ignites or explodes very easily in air.
https://en.wikipedia.org/wiki/Hydrogen_safety

Hydrogen is not that useful as a fuel at the moment except in specialty circumstances. This is because our cheapest source of it is hydrocarbons, which are already fuels themselves. It has plenty of other uses, in particular we need it for the ammonia production that has done so much for the increased productivity of modern farming.