There's a minibus, private service (which you've already mentioned) or a taxi stand.

I prefer Mai Linh taxi. Here are some links to more information.

https://www.travelfish.org/orientati...hanoi/hanoi/23
http://hanoikids.org/identify-a-reliable-taxi-in-hanoi/
http://wikitravel.org/en/Hanoi#By_taxi
http://www.hanoiairportonline.com/public-taxi/