Your statement regarding options is entirely accurate. You can indeed hedge a long position in futures or in shares by either writing a call (a partial hedge) or by buying a put (an insurance hedge).
Your question: In the futures market, would I purchase a contract to protect my downside? is unfortunately inchoate. Before it can be answered, one must know your present-day position in whichever market. If we're considering these housing/real estate index futures, and assume that you're a homeowner, then the answer is ''yes'', you might indeed sell short, not purchase, some number of futures. The contract size is $50,000, so a nominally ''perfect hedge'' (somewhat of a misnomer, but that's another discussion for another day) of a home appraised at $250K in, say, Chicago, would be the sale of 5 contracts on the Chicago-area index.
The term ''natural short'' refers to those who would use a futures market only from the short side. A wheat grower has wheat to sell, sooner or later. He or she can lock in a price for the wheat to be grown by using the futures market (i.e. by selling the wheat in advance of its production, for delivery in future). This is the wheat grower's ''natural'' use for a futures market, hence the term ''natural seller''.
There's a different term for wheat growers who buy futures: they're called ''Texas hedgers'', which, trust me, is a term of considerable disdain. After all, the wheat grower already OWNS, or will shortly own, some amount of wheat; to buy futures means that he or she may own even more in the future.
There's a technical term for these folks: gamblers.
Possibly the best way to view the difference between futures and options is to consider that, in a futures contract, the goods are already sold (on the one hand) and bought (on the other) the moment the trade is made. Delivery of the goods from seller to buyer may or may not take place thereafter (doesn't, in the vast majority of cases), and btw the decision about delivery (in delivery-settled markets such as wheat) is entirely the seller's.
In an option contract, no purchase or sale of goods is made at all. What has actually traded are a set of rights and obligations. The option writer guarantees to sell X amount of Y goods at Z price on or before date D (if he's written a call) or to buy X amount of Y goods at price Z on or before date D (if he's written a put), at the option buyer's demand. If the option buyer, for whatever reason, makes no such demand, the writer pockets the premium received and goes out and has a nice dinner.
Of course, the typical reason for an option buyer to NOT demand specific performance from the writer is that the price of Y is unsatisfactory, at or near the option's expiration, from the option buyer's viewpoint.
The ''cash flow'' is exactly as you say: he who buys pays, he who writes collects...but may have to pay back substantially more in future, depending on how the underlying market moves.
In futures trading, there is NO -- zero -- cash flow in either direction until one party has liquidated the position. Indeed, the position may be liquidated and re-liquidated any number of times (I know, that sounds screwy, but it's literally true).
To avoid the awkward bookkeeping that this condition of contest implies, the exchanges perform a daily 'mark-to-market' of all traders' positions. This procedure may or may not require any given futures trader to provide more capital (the infamous ''margin call''), according to how the trader's various long and short positions have fared during any given day.
Naturally, I've elided some details here, and my apologies for that, but I hope this post is some use to you regarding your questions.
And, btw, good trading to you!
LOL! I've literally turned around some S+P contracts in 30 seconds. Those were on 'crash days' when you were just 'catching' freefalls below major support.