If mic self-noise is truly a concern for you, then look beyond Zoom. This page provides a good comparison:
I have the Sony PCM-M10 and a Tascam DR-680 for different purposes, and both are solid units for there price. Keep in mind that most portable recorders will not give pleasing results for "far away sources" unless you mean general ambient recording. For distant sources you would need a specialized microphone. For most versatility, I personally would recommend choosing a recorder with XLR inputs such that you can buy additional mics in the future. The Olympus LS-100 seems to be a favorite among recordists on a budget for this reason.
If you want the advice of people far more experienced with these recorders and techniques than myself, I'd also suggest signing up the for the nature recordists mailing list. It's a very useful resource in general.