"For now, they say, real-estate sales are about the only potentially profitable economic activity on the Moon — certainly more practical than trying to make money by mining its minerals. They note that many have already paid $19.95 per acre for “deeds” to lunar land even those these are novelty items that have no binding legal authority.

Presumably, Mr. Wasser and Mr. Jobes write, people would be willing to pay more to speculate in land legally owned by a company established by a small group of settlers who had staked a claim to 384 million acrees — an area the size of Alaska, which was successfully claimed by Russia after a small fur-trading settlement of fewer than 100 people was established in one spot there. If the land went for $100 per acre, that would amount to nearly $40 billion. "
http://tierneylab.blogs.nytimes.com/2008/08/29/for-sale-moon-and-mars/

I don't think that 100 or few people should be able to claim "384 million acres", though a few million acres might be a more reasonable claim in terms of upper limit. Though if less than 100 people were living on the Moon for several decades perhaps up to tens of millions of acres might be reasonable as upper limit.
But I think some areas on the Moon could be priced much higher than $100 per acre, perhaps as high as $100,000 per acre or higher.

The amount of land in which could claimed should based upon current use and potential use within the term of say 10 or 20 years.

What we don't want is monopolies on some particular type of areas such as where there is almost constant sunlight or craters in which have a high concentration of water ice. Though we should grant claim to some of these areas if these are discovered and used. So there might different scales of land for say peaks which allow nearly constant sunlight and direct communication to Earth- one party, entity, enterprise may be able to claim say 10 acres of this type region compared to hundreds to thousands of acres of crater bottom land which has minable water. Whereas say the enterprise involved areas of land for radioactive material storage one might "use" or plan to use a larger area- +100,000 acres. The larger areas might also include areas in which one wishes to have an observatory or manufacture thing requiring the lunar vacuum or large solar farms. Or one is building large capital investment of a "spaceport", Ie, coil induction mass drivers.