There are a few important parameters and sizing specs one needs to pay attention to when selecting a front derailleur. One would be the way the derailleur attached to the bike. Many are band clamped to the seat tube and the band clamp of the derailleur must be the same size as the seat tube. They also make shims that reduce a 34.9mm band clamp down to the other two common sizes, 31.8 and 28.6mm. Shimano also attaches front ders via a high direct mount bolt where the frame incorporates a spot on the frame's seat tube for the mounting point. In addition a third possibility is an "E-type" derailleur that attaches to a bracket held in place under the lip of the bottom bracket cup. Related to these are the "E2 type" aka: "low direct mount" derailleurs that attach to posts built into the frame.
The next parameter to consider for correct replacement is the size of the outer cage of the derailleur, the shape of which must match that of the large chainring for good shifting. Basically this is determined by the number of teeth in the large chainring. The specs of a proposed derailleur should list a range of what number of teeth the derailleur is spec'd to handle.
There are other not insignificant considerations in selecting a front derailleur. For your application the front derailleur must be a mountain triple, meaning for a mountain bike with a triple front chain set. Also necessary to get right is whether the current derailleur is top-pull or bottom pull which refers to the direction from which the inner cable is drawn to move the derailleur. The design of the bike--essentially where the cable is routed--determines which sort of pull you'll need. If the cable is routed underneath the bottom bracket shell via the down tube, it will come up to the derailleur's pinch bolt from the bottom, when the shift lever is thrown, the pull of the cable is downward, and thus, a derailleur must be a "bottom pull." Conversely the cable can be routed across the top tube and then turn down to a stop on the seat tube where the cable then approaches the derailleur from the top, the cable is pulled upwards and thus this bike will require a top pull derailleur. There are derailleurs that are "dual pull" which can handle either a top or bottom mount cable routing. Shimano's newest front derailleur's are "front pull" derailleurs. These utilize a full length of outer housing from shifter to derailleur and so any design of bike frame can use them, although some newer bikes may have cable guides for front pull derailleurs.
Regarding the "speed" of front derailleurs, this is for the most part a marketing term as an otherwise compatible front derailleur from 6 thru 9 speed will work. It's best practice to stay within +/- 1 speed class of the system since as the number of rear speeds increase the front spacing narrows a bit (as does the chain) and the distance between inner and outer cage plates narrows as well. In practice, for a 7 speed system an otherwise compatible 6 thru 9 speed triple front derailleur will work.
There's a lot of information here so I'll link you to some pertinent articles to get things straight:
Background on types of front derailleurs
Shimano Front derailleur specs.
The latest front derailleur offerings for 7/8 speed drivetrains begin with the "Altus" models numbered in the FD-M3000's and down. Shimano stamps the model number of the front derailleur on the inside of the inner cage plate. It will look like, "FD-Mxxx" where x are numbers. The link above is the list of the latest (last 1 to 5 years of production) front der specs so yours may or may not be listed. There is a link within the website to historical documentation within which all models are somewhere revealed.