I don't know how much you know, so I'll summarize this briefly. You want two things in a sword, hardness and ductility. Hardness keeps the steel in it's shape. A hard blade will keep it's edge and will not take a bend. Ductility preserves the blade. If a sword was made from diamond, it would shatter. If a sword is not ductile, its edge will chip and the blade itself will break. Unfortunately, the two are inversly related. On the chemical level, more carbon makes the steel harder.
The phrase "carbon steel" is (depending on your point of view) either an oxymoron or redundant, as steel is by definition, an alloy of iron and carbon. "Carbon steel" generally refers to steel with iron, carbon, and nothing else. You have two main variations of this that are used for swords. 1050 steel has .5% carbon and the rest iron. It is an easy to work with, nice steel, but it is really too soft for practical blade use. Significant hardening is needed to make it useful. I know of no good swordsmiths who use 1050 for the edge of a blade. It can be done, but why add unnecessary work?
Then, there is 1065/1075, with (you guessed it) .65% and .75% carbon respectively. 1075 is a good starting steel for swords, though it will still need hardening, you have a higher starting hardness throughout the blade, so it doesn't have a tendency to case harden (where the outer layer is hard, but the inside is soft). 1075 is a commonly used starting steel, and I have heard of katana forged with a 1075 edge and a 1050 spine. There are a number of other, more complex alloys that work well with swords. Read into it.
Now stainless has chromium in it, up to 25%. Above 1% chromium makes steel brittle. Stainless isn't bad for knives, as the steel isn't put through too much strain, however, swords put way too much strain on the blade, and they snap or shatter. There are some non-rusting alloys that aren't brittle, such as the maraging steel in fencing blade, but they are too soft to hold an edge.
One final thing, look into hype before you buy. A lot of the information available is obviously biased either for or against certain smiths (The best example I've ever found is this: On an otherwise very informative page, the review of S7 on is a clear attack against Angelsword
). No one is unbiased, so take nothing on faith. For example, that page I mentioned earlier is very informative, but one of it's main deciding points is which steels can show hammons well, which in my opinion, is rating appearance over the actual strength of the blade.
Caveat Emptor, may the buyer beware