On buying bated swords for fighting mock duels or training in the art of defense
The following is relatively SCA-centric, since that's the organisation I fight in, but the principles should be similar for any sword intended for sparring regardless of the specific rules you're playing under. If you are in the habit of going out and swinging three-foot lengths of steel at your friends, I presume that you are doing so under the aegis of some sort of organization, which has their own set of safety rules and standards. Their rules obviously supersede the ramblings of a random stranger on the internet. When in doubt, ask your local marshal/fencing master/expert.
In the Society, the term "fencing" has stretched at this point to cover any form of sword combat fought with blunted steel weapons by unarmoured* combatants, not just Renaissance-period rapier combat. As a result, it presently includes earlier styles such as two-handed sword work and 13th century sword-and-buckler techniques,** and various sword types including curved blades such as sabres and katanas. At this point we probably should just start referring to it as "swordfighting" or something, but that's a whole different kettle of fish.
These weapons are intended for sparring, so the blade isn't sharp and isn't supposed to be. As a result, there is no need to find a balance between a springy, relatively soft steel spine and a hardened edge, and the entire blade is usually made from some variety of high-carbon or alloy steel. One-handed swords most commonly use a 35in blade (measured from the grip to the tip, not including the tang), although 38, 40, and even 42in blades seem to be increasingly popular - personally, I think 42in is more than a bit silly on a one-handed sword, but some of the really tall fencers seem to like them. Again, within the constraints of the rules, find a blade length that's comfortable to use. Two-handed swords obviously may have even longer blades: I've seen greatsword blades advertised up to 52in.
The cross-section is typically oval or diamond-shaped, and the blade tapers from hilt to point. A diamond cross-section gives the blade a more authentically period appearance, at least for a 16th c. rapier; otherwise they are not significantly different in terms of performance. Alchem makes blades that are just flat steel with a rounded edge and a more pronounced taper, which gives them a much earlier period look. All of the curved (katana or sabre style) blades I've seen have a flat cross-section.
There's a fine line - which is largely up to personal taste - between a blade that's flexible enough to hit your friends with, and one that's excessively whippy. The blade must have some flexibility to absorb the force of a direct thrust; even a few pounds of force behind a 3/4" diameter blunt is quite enough to leave a nasty bruise. On the other hand, if the blade is too flexible the point will wobble and be hard to control. This is especially a problem with long blades - the same steel, thickness, and cross-section that make a perfectly acceptable 35in blade may well make an excessively floppy 40in. One of my local marshals has a theory that flexible blades are more likely to fail and will fail faster than rigid ones because the constant flexing weakens the metal in much the same way that bending and straightening a paper clip will eventually break it. Anecdotally, there may be some truth to it - the only blade I've had fail was a fairly flexible Hanwei that only lasted about six months - but so far no one I know of has any real data on blade failure rates.
The blade should have a full tang, meaning that the metal of the blade should run the full length of the hilt; this is stronger and more secure than having the blade socketed into the hilt, and means that the pommel can be securely fastened to the end of the tang. Typically, the last few inches of the tang is threaded and the pommel is screwed on, although I do know of one swordsmith who makes flat-tang blades and attaches the pommel with a spring pin. Threaded pommels tend to work loose after a while, but are very easy to disassemble if you need to replace the blade or any other parts. The tang and blade should be forged as a single piece; any welds are a potential weak point.
This is very much a matter of personal preference. The grip should feel comfortable in the hand, and beyond that it's mostly aesthetics. Most people find that a round grip shaped like a cylinder or tapered cylinder isn't very comfortable to use if you can't curl your fingers around the ricasso; it tends to turn in the hand, so you end up holding it tighter, which is tiring and less flexible than a looser grasp.
The variation in guard styles is nearly endless, from plain cross hilts through various side rings and knuckle guards up to fancy swept and cup hilts. This is mostly a function of the style and period of the sword: a katana will have a tsuba, a 16th century rapier will have a swept or cup guard, and so on. The late period European guards do have a couple practical advantages. Since they extend a couple inches in front of the crossguard, the fencer can wrap his fingers around the ricasso, which provides a stronger grip, and the guard protects the sword hand. However, with practice the quillons will serve to protect the hand very effectively, so if a late-period cup hilt rapier doesn't match your style, there's really no compelling reason to use one. (The only reason I even own a swept-hilt rapier is because it was given to me; my area of interest is the Principality of Antioch in the 13th century, so I much prefer using a sword that at least looks like a Crusader longsword.)
The crossguard on a swept- or cup-hilt rapier is frequently curved, either a "C" curve, where both ends bend forward toward the blade, or an "S" curve, where one end bends forward and the other back. A forward-curved quillon is useful for catching and controlling an opponent's blade (or even disarming him).
If you're likely to need to use the sword in either hand (if your rules allow for disabling limbs, or you expect to fence with case of rapiers), you may want to consider an ambidextrous setup in which the guard is symmetrical. This is not entirely necessary; my current rapier has a right-handed guard, but is perfectly comfortable and effective used left-handed.
The Overall Weapon
The balance of the sword is a function of its centre of mass. If the centre of mass is very close to the hilt, the sword will feel lighter in the hand. It will require less strength to wield, and it will be easier to control. The further along the blade the centre of mass moves, the more tip-heavy the sword feels. This requires more wrist and forearm strength, but gives it more momentum behind beats and parries. Some fencers strongly prefer one or the other; others swap back and forth depending on what feels better on a given day.
The type of sword you use will affect your fencing style (or possibly, you should choose a sword that matches your style, depending on how you choose to look at it). A katana lends itself to a close-range, slash-based fencing style, while an extra-long rapier lends itself to point work. If you use a lot of binds, you may want to consider a C-curved rather than straight crossguard. The combination of weight, balance point and grip means that different swords handle very differently; in the end, within the bounds set by the rules, the sword you want to buy is one you want to use.
As with any substantial purchase - a bottom-end rapier runs about $120 (US), and they go up from there - it's a good idea to play with it a bit before putting down any money. Pick it up, see how the weight and balance feel, make sure the hilt sits comfortably in your hand. If you can't manage that, find someone who already owns one from the same maker and see if you can borrow it.
What you do with the sword once you've bought it is entirely outside the scope of this writeup (which is quite long enough already), but I'll add a couple notes on the care and feeding of rapiers. Since the steel of the blade is not stainless (stainless is too hard and inflexible for fencing blades), it should be kept dry and clean. Any rust should be cleaned off as soon as possible. The edge will inevitably get nicked and roughed up in combat. A rough edge can catch and possibly tear an opponent's clothing, and can weaken the structure of the blade, so they should be smoothed out. Small nicks can usually be buffed out with steel wool or sandpaper, while deeper ones will require the use of a file.
*"Unarmoured" as in not wearing heavy leather or metal armour; fencers are nominally assumed to be duellists wearing street clothes, not armoured combatants on a battlefield. In the interests of not actually killing anyone, suitable protective gear is obviously a good idea.
**The earliest extant manual on European sword-fighting technique is the I.33 manual, which dates to about 1295 and describes a sword-and-buckler style clearly being practised by combatants in ordinary clothing, not armour. I haven't had a chance to pick his brain for the details, but one of the fencers in my area has documented mock fights fought in street clothes with blunt swords back to the beginning of the 13th c.