I understand why this can be confusing. Here is a rundown including some economics 101 concepts that tries to put it all in perspective.
To understand the lifecycle of PoS and how it distributes, we should discuss PoW mining again. In PoW, there is a fixed number of blocks but not all are "known" at the start. The process of discovering the block is what gives you the claim. Because blocks become more difficult over time, early adopters can mine a large quantity with a low capital expenditure(no fancy ASICs needed for those early blocks) or cheaply trade for their currency when its valuation is low, while latecomers have to either spend big to mine, take a smaller return by mining in a pool, or trade at higher prices. None of these options will get them ahead of the early adopters.
So, we can see, the time you enter is the most important aspect of PoW, with respect to what % of the total money supply you end up with. The aspect of spending CPU time to unlock new blocks is a secondary concern and is mostly influential if all the existing big holders are unwilling to distribute any of their holdings. The value of the currency as a medium of exchange ultimately comes from whether people "believe in its worth." Nothing about the piece of paper fiat is printed on is special; it's the trust that the society places in it that gives it value. Cryptocurrency is ultimately the same, but it has a fancy high-tech method of guaranteeing ownership.
In pure PoS as done by Nxt, PoS is there mainly as the technology to enforce ownership within the system, not as a mechanism to change quantity or distribution of currency. Early adopters still enjoy big benefits just as in PoW. The difference, economically speaking, is that you MUST trade to get any currency now. This makes Nxt potentially more brittle, since nobody can enter independently and mine on their own to add supply - you're dependent on the founders being willing to trade or give away. As long as people are buying, and able to buy, the currency will gain value, since more people have invested in the same nominal quantity. That's deflation in action - the same amount as yesterday represents "more wealth" today.
If the market stops moving, though, because everyone's hoarding and expecting more wealth tomorrow, nominal value will be high, but nobody will be able to exit the currency - that's a liquidity trap, and it will cause panic selloffs as people start taking a lower and lower price in order to get anything out. This can also happen in PoW, but it's less likely as long as the currency can be mined, since then the lower bound on value is the energy cost of unlocking a new block relative to how much currency it gives you - if you're the person who mines the block, you should be able to, on average, break even on your effort, and in doing so you inflate the currency.
Liquidity is one reason why economists tend to prefer considering mildly inflationary currencies within the larger economy. Inflation gives speculators a reason to keep trading, because then the speculator will see that some other asset might be a better store of value at any given point in time, and try to move from one to the other. ("How do you gain a small fortune? Start with a large fortune...") As well, debts are also hugely influenced by the value of a currency, and if the currency deflates, debtors lose, as their debts become impossible to repay. This in turn disrupts the rest of the finance system that was relying on debt collection, etc... Long story short, deflation gives you a very wild ride. Most of the coins out there attempt have inflationary characteristics similar to gold - not zero, but low enough that it is still deflating relative to fiat.
As you might have already realized, inflation isn't perfectly distributed either. A profitable miner might succeed in bootstrapping to a larger and larger operation, outpacing competition and dominating the market. In that case there truly is a "rich get richer" effect, where the early advantage compounds to a disproportionate result. (this probably isn't true of PoW in practice; I haven't checked.) Likewise, a central bank might want to release new fiat currency to inflate, but their options for distributing it are usually limited to lending to the biggest banks, and those banks in turn generally have freedom to apply their new currency in ways that may or may not facilitate the economy - moral hazard is rampant when dealing with the innermost aspects of a fiat system. And inflation ultimately affects the price of goods and services, but price changes won't all appear in the system immediately just because a bank got more money.
In any case, with all of those examples, the inflation isn't appearing all over at once; it's crude and lumpy and makes our understanding of the economy chaotic, since the "starting point" of money is going to influence how it's used and valued. Economists tend to construct oversimplified models to sweep the issue under the rug, rather than do something as utopian as propose making our actual currency better.
So, knowing that Nxt has no inflation, we can see that Nxt may suffer from low liquidity and become problematic for use in day-to-day generic debts, compared to existing coins, but it also won't suffer the exact downsides of "bad" inflation. The other features complicate the picture. It's power-efficient, since it's all PoS, while power consumption will increasingly become an issue with Bitcoin and impose an overhead on its use(this aspect is addressed by Peercoin). Coin coloring will be built in, which means that Nxt can become a representational unit for ownership of something else, where the else is any kind of asset. That use-case makes Nxt more of a "store of value." Other upcoming things like the built-in exchange will all add value to the currency as a whole, since it negates the need for those services to be provided by independent (potentially untrustworthy) parties.
So, in terms of "what should I be thinking as a speculator," think about what kinds of things Nxt does well, better than other cryptocurrencies. Will they be enough to make people trust it for their business? This is a world where many kinds of cryptocurrencies might be able to succeed, at least for a while, because they're so easy to create. I wouldn't expect any of them to last forever, though, since there will always be something that could be tweaked.
