Which nails should I use for shoe molding installation?
Definitely the Brad nails.  The finish nails will leave larger holes (16 gauge vs 18 gauge usually) and will be more likely to split the wood.  Based on the size of your shoe, i dont think you could use pin nails (18-23 gauge).

The Big Box home improvement store always sell kits with finish, brad, and pin nailers for pretty cheap.  Some have 2 guns, some 3, and some come with other stuff.  I've always found that the best way to go.

Just did a quick check for some kits.  Home depot 3 piece Kit for $99.  I have had good luck with the Husky Brand from HD.  Lowe's had some kits but they were name brand and a lot more expensive.  Could also check out Harbor Freight, their stuff is definitely cheaper quality, but maybe that is ok for your situation and usage.