Should I use a carpet kicker or stretcher?
In a normal room-sized install, both tools are used.  The kicker for the first edge and the stretcher for the rest.  Kickers are also used in corners where the stretcher is awkward to use.  On stairs, just a kicker is used.


A kicker is ideally only used to attach the carpet to the tack strip.
A stretcher is used to attach the unanchored sides.  You anchor it at an attached side and stretch the carpet to the opposite side.


A pro would use a stretcher as much as possible.  A carpet that has  been kicked with a reasonable amount of effort will pull up at the edges from any typical abuse.

A small space like 2x3 would have only used a kicker - which is why they invented the mini-stretcher (like this one).  They're not cheap for a single job and I haven't seen one for rent, but it's worth a few calls around.

That's not to say you can't just use a kicker, and I probably would if I didn't have access to a mini-stretcher.  You can do a 90% job in a small space with a kicker, but you'll definitely work up a sweat.  

FYI: For larger jobs, even with maximum effort, the smaller head of the kicker will lead towards ripping the carpet if you try to get the same amount of stretch as the power stretcher will give you with no effort.