What kind of wire should I use to pigtail an outlet?
Depends. 

If  you're using "screw-to-clamp" type receptacles

Then your "go-to" is #12 stranded THWN-2. These are sold as individual wires.  Also #12 solid bare or green ground wire.  (ground wires need to be pigtailed regardless, so you may already have this.) 


The stranded wire is much easier to work with (push the pigtails into the back of the box and the receptacle will slide in like a dream), but its downside is it's difficult to attach to screw terminals without a lot of practice, and catastrophically dangerous to use on backstabs. I actually saw this fail once. 
Stranded wire wire-nuts just fine to solid wire.  No pre-twisting, just line them up evenly and twist like the dickens. 
#12 is the "universal donor" that will work on both 15A and 20A circuits. It's a little stiffer -- oh wait, it's stranded! 


If you're using screw terminal type receptacles

In that case, ditto ditto ditto solid wire.   Which will be stiffer, but cake to put on screws. 

However, if you want to buy all of them in one single SKU, buy "#12 Romex" aka NM-B type cable.  Buy 2' lengths at a time and cut into three 8" long sections (or four 6" sections), then carefully exacto-knife off the sheath by cutting directly down the ground wire (so you don't nick the insulation on hot or neutral).  Voilá, pigtails. 


The disadvantage of NM-B is it's not legal outdoors.  For that, slicing up UF cable is challenging, so I'd go back to THWN-2 wires. 
The individual wires are not marked, so you cannot use them for conduit runs. 


Don't ever buy #14 for pigtails, because at best  you have an "orphan" you can only use on 15A circuits, and at worst you accidentally use one on a 20A circuit and have a problem. 

If you're using backstabs

Stop.  They are unreliable and cause most dead-circuit problems.