Wow. Whole bunch of stuff going on in this post...
Of the three HB's you listed there is a very large difference between them (guessing that you'll be looking for the DI versions). All the units are black and white LCD screen, and are backlit. None of these screens are HD by HB's standards, but one is close - the 581.
The resolution on the 561 is terrible. 320x320, which is bottom of the barrel when compared to many units out there.
The resolution on the 571 jumps to 320x640, which helps, but still kills your vertical resolution which is most important. The unit is also available with both the 2D and DI, but does not have a GPS for mapping.
The 581 has a 640x640 resolution for nice, sharp imaging. It also has both 2D and DI which is preferable. It also has the GPS (581i DI), which is very helpful, but the unit does not have any maps loaded on it's own (a base map). In order to see contour lines and things other than the shoreline, you'll need to purchase a 3rd part card of your choice based in your area for the best results.
If you could swing it, and are willing to deal with a B/W LCD unit (which it sounds like you are), I'd go with the 581 and be happy as punch. It'll do everything you need and you'll still have money in your pocket vs the larger fancy color units.
I love me some fancy color FFer's though. :lol:
Lowrance has options also, but you asked about HB, so there you go. For what it's worth, HB owns the multi frequency fish finder market under $500, and for good reason - Lowrance is taking notice.
-EDIT-
Saw you went with the 581i - you'll love it. Great choice. If I could go back to a B/W unit, that's the one I'd use.