Genealogy search in USA

[Sailor]

Gents,

For years i've done some genealogy search of my family. I haven't been so active with my searches but rather do it whenever i have no better things to do and when i am able to leave my general laziness.
It is relative easy here to track ones ancestors, as we have good records at least until 1600- 1700. It is usually possible to go even further, but that takes a lot of efforts, some traveling and the ability to understand old difficult texts. The hardest part is with people who died over 100 years ago as not all had last names, or then they were named after the place they lived or after their fathers (or mothers in case that father was unknown). My last name in English is somewhat like 'place of many dry meadows' and my wife was just 'the daughter of Henrik' before taking my name.

However. During the history some of my family members have moved to USA, and got into oblivion. That happened so long time ago, latest of my family members that got there and never came back was 1907 so she is surely dead.
Recently i thought that maybe it would be fun to try to find if i still have some distant relatives there. I've lurked some US genealogy sites but as i have no any experience of them, i decided to ask the one and only place where i could possibly get a good answer, here on SRP.
So, Gentlemen, have you any experience from genealogy search in USA and what are the sources you suggest.