It depends on whether your primary interest is U.S. or British English.

As a U.S. English speaker, I really like the American Heritage Dictionary a <em>lot</em>, because it is about the right size, because I find the definitions to be really clear and well-written, and because I like its usage notes.

For me <em>the</em> final authority will always be Merriam-Webster's Third New International, Unabridged, but that's far too clumsy and bulky for a home dictionary. The Merriam-Webster abridged editions are nothing special.

I do not know what the "Random House Webster's" would be and I don't trust a title like that. There used to be a very good "Random House Dictionary," edited by Stuart Berg Flexner, but I'm pretty sure it's out of print. Merriam-Webster is the "real" Webster's.

Hi, Dan

Thanks for your input! Both of the major varieties of English(that you have mentioned) draw my attention, however, you can subsume my 'primary interest' under the category of English.

The Oxford Advanced Learner's Dictionary has been a long-time companion, but my profession compels me to flit from one dictionary(British or American) to another.