I have two Tech. IIIs, and I love them.
For most things other than studio work or other close-up work, it is probably not the movements on the camera that will limit you, but the lenses that come with it. It's a capable camera for many things, but those particular lenses limit you quite a lot. They are designed for shooting hand held straight on or with very minimal movements. To get the most of what the camera can do on a tripod, you need lenses that are designed to allow more movement.
What the seller is saying about the numbers matching only affects you if you want to shoot hand held, and even then, it is possible that you will be "close enough" in some applications. The matching numbers ensure proper focus with the rangefinder. Hopefully the 240 is numbers matched to the cam and camera body.
Oh yeah. Matching numbers also affect market value somewhat significantly. Buyers know that these cameras need numbers-matched parts to be usable hand held, and they will pay a premium for this.
These cameras are compact, but they are far from light. They weigh 6 to 8 pounds, depending on what you have mounted to them lens wise and back wise. My SINAR F1 monorail with 12 inch rail, rail clamp, DB shutter, and 210 f/5.6 lens weighs about seven, and it has every movement under the sun, and is actually fairly easy to backpack with. The advantages of the Linhof are only that it is compact, and that it is quick to set up, not to mention the obvious fact that the SINAR is not hand holdable.
There were five versions of the Tech. III, and only the last two have the dropping bed, which gives you the ability to employ front forward tilt. MAKE SURE you have this if you have this if any intentions to use front tilt, or to use a 90mm lens in vertical orientation without taking a picture of the end of the bed.
The rear movements are 15 degrees any way you want.
If the camera is in very good shape, I think $550 is about right or maybe a bit high, personally. Maybe I am lucky, but I got two incredibly clean, original owner kits with six lenses (three each, every single one of them number matched to the original camera, with the proper cams), tons of accessories (including a roll film back and an optical zoom finder, a custom fit case for one of the kits, four Linhof Deluxe film holder, and 13 standard film holders in like new condition) for $1650 total. These are really collector-quality cameras the way they came, and I feel that I got a lot for what I paid. Strangely enough, they both fell my way within a matter of months of each other.
One thing to watch out for is the bellows. They are old for a flexible leather item (55 years old, at a minimum, unless they have been replaced at some point). Leaks are often a problem, and replacing them AIN'T CHEAP AT ALL!
I think it is a great camera for most things. It is versatile, compact, and well made. I wouldn't use it to photograph most still lifes or products. You can do some architecture with its capabilities, but not that in which the most extreme of image distortion is desired. It is a great camera for shooting people, especially if it has a cammed 240 lens, and it is great for landscapes too.
You will need some sort of viewfinder to use it hand held, and they prove to be rather expensive, even on the used market. They range from $150 to $350 depending on model and condition (which is why I was so lucky to get one in one of the kits I purchased).
You also want to see if it has a hand grip or at least a leather strap. Some have neckstrap lugs as well, which is a great help, IMO. (Only one of mine has them.)
Lens boards are specific to the III (and possibly the II, though I don't have any idea). They will not work on any of the later models (IVs, Vs, etc.).
As for the specific movements, this is what you get:
Back tilt, 15 deg. forward or rearward
Back swing, 15 deg. clockwise or counterclockwise
Front rise, about 4-5, maybe 6 cm
Front fall, some, but very little
Front lateral shift, about 1-1.5 cm either way
Front swing, 10-15 deg. either way
Front rearward tilt, 15 deg.
Dropping bed (versions 4 and 5 only), 15 degrees
*Dropping bed, front rearward tilt, and front rise can be used together to provide front forward tilt of 15 degrees
Triple-extendable bellows