If they are early 20th century or before, there is the possibility that they're an earlier key system that should NOT be foisted off on a modern student, especially a beginner who wouldn't know the difference. Fingerings for a few notes can be somewhat different, and a student shouldn't have to learn obsolete ones. The clarinets may still be usable by a casual player who doesn't intend to "study" at it.

Comparison with a currently "modern" clarinet to see where the keys/holes/rings are located could be done by any reasonably informed player, with a modern insrument for comparison.

The "loose joints" would likely be easily remedied by new "corks" at the joints, and might even be helped by a liberal application of "cork grease" if they've been without lubrication for a fairly long time.

A "looks like wood but isn't" would likely be a "resonite" (plastic) material that didn't appear in very common use until ca 1955 or later, so the key system probably would be "modern" although it should still be verified.

A clarinet that hasn't been used for a year or more most likely should have a complete "re-pad" which is a simple, but time-consuming, repair. You need a player sufficiently practiced to tell you if it's playable as is, since an unpracticed player won't be likely to know the difference between "skill failure" and "leaky pads." The cost of getting a re-pad done can range from "reasonable" to "ya' gotta be kidding me."

For a casual player who just wants to "play along with the gang" the different tunings can be accomodated to some extent by simply not fully seating the mouthpiece in the neck, or not fully seating the neck on the upper body, either of which will lower the pitch. Concert orchestra players at high-school and semi-professional levels commonly use one clarinet with interchangeable neckpieces, one for Bb and one for A, with satisfactory results, so "tweaking" the tuning should work just fine for the difference between an old "high A" instrument and a "modern A" one. (You will need a good "cork" at the joint where you make the adjustment, so that the parts stay where you put them.)

Always be sure to thoroughly "wet" the reed before beginning to play. Experienced players usually just "slobber it up" but for a beginner dropping the reed (removed from the mouthpiece) in a cup of water for a few minutes usually will suffice.

Also be aware that although the teeth support the lip that controls the reed, you should avoid "biting down" to get your tone. You can end up with a badly mangled (and very tender) lip if you allow the "bite" habit to develop. Lip muscle tension will do it, once you figure out how.

John