1/4″ quarter round 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.

Most molding (skirting board) is 3/8" thick. You need a 1/4 inch gap around the floor to allow for expansion due to moisture. So if you're going up right against the drywall, you'll have a problem with getting molding thick enough to cover it (minor variations in the gap WILL show).

One alternative is to buy the stuff they sell as window/door casing which is usually closer to 3/4" thick on one edge. This is a bit pricier, and can look a bit heavy.

An attractive alternative, which can give you a nice look is to use door stop instead of quarter round. This is basically the same as using quarter round, but it's smaller and lighter, and doesn't encroach on the floor as much.

However, if your drywall doesn't come all the way down to the floor (usually a basement scenario) then as long as you have that quarter inch gap under the drywall free and clear, you should be ok with just ordinary skirting board.