For example, an English Learner's Dictionary usually has a nearly exclusive list of vocabulary that is employed in defining the corpus. I am looking for something, more or less, like that in Japanese. I am already studying from Core, which I guess is pretty basic and builds up, but I thought something like this would be very useful anyway. Anybody?

Why would you want to buy a dictionary that will be very quickly prove to be woefully inadequate? Which words are frequent will differ depending on the type of media and subject matter. Words used frequently in fiction will differ from that used in the news or on internet forums. You're better off buying a decent electronic dictionary which can serve you for years to come. If you're talking about that 500 words that make up 80% (or whatever the number is) of words appearing in any random sentence, then just go read anything and you'll learn those words very quickly. But keep in mind the it's the remaining 20% of words in the sentence that will carry 80% of the meaning and those words are drawn from a much much larger corpus, which you'll eventually want to learn.

If you really want a list though, a web search for N5 vocabulary will give you an arbitrary selection of 'basic' vocabulary.

Core 2000 is pretty decent although not graded very well (at least it wasn't in the old smart.fm)

The old JLPT4 vocab list is also decent: http://www.jlptstudy.com/N5/index.html

@nadiatims I was not considering buying a dictionary, just looking for a vocabulary list, but now that you mention it, do you have any specific advice?. I like your 'go read anything' but I am afraid it just doesn't work, too painful, it's like i+100 rather i+1.

Thanks @caivano. This is excellent.

The JLPT word lists are graded pretty well. Much better than Core anyways.
If you want something readable as a beginner, get a textbook like Genki.

Indeed, read through a beginner textbook or something. That or a anything with translations, phrase books parallel texts etc. i+100 isn't as tough as you may think if it's in a format where the meaning of the words is easily accessible, and hey more unknown words means more to learn. You can just go read wikipedia or something with rikaichan. Just accept that comprehension won't be 100% at first. At first it's like i+100, then a week later it's i+90, then i+80, and before you know it you have a lot of the most common words down and comprehension and reading speed has quadrupled. If you insist on i+1, you'll be using learner materials forever. You can even learn from subtitled videos (despite what some people say).

Point taken.

I am 'enjoying' Core at the moment, finished 1000 and made it to half of 2000 so far. It's getting a bit tougher with 3 Kanji words now.