The operas in this set are:
La fanciulla del West
Il trittico (The Triptych, or the three one act operas that were intended to go together):
This set is in some ways easy to review, as it is a collection of solid performances at an unbelievably great price (typically, Amazon sells this for about half of the low retail price of $49.98, or, in other words, about the full price of one opera). The sound quality is quite good considering when it was recorded, and is good enough to be rewarding on a good stereo (I played this set through some Apogee Stage speakers; just do an online search for reviews of these speakers). Really, if one is on a tight budget, this is well worth getting as one's only set of Puccini operas, and if one is rich, one ought to buy it for comparison with other performances.
But it is not an ideal set, for several reasons. First, as others have noted, there are no libretti. So if you are the sort of person who wants to read along as they sing, so that you will know what they are singing, this is a significant drawback. Even if you obtain a copy of the libretti elsewhere, there will be no markings in it to tell you what track the passage is on, so if you get lost or just want to know what they are singing at a particular point in the opera, you may have difficulties finding what they are singing.
Second, although the sound quality is very good, it is certainly not the best, and certainly not state of the art. So if one is very picky about sound quality, then one might want to look elsewhere (and, if one is that picky, one ought to generally avoid recordings this old, as this sounds better than one ought to expect for that time period [1950's to early 1960's]).
Third, although the performances are great, and deserve 5 stars generally, they are not all the best that money can buy. The three operas recorded by Pavarotti in the early 1970's Puccini - La Bohème / Freni, Pavarotti, Harwood, Ghiaurov, Karajan, Puccini - Madama Butterfly / Freni, Pavarotti, Ludwig, Wiener Phil., Karajan, & Puccini - Turandot / Sutherland · Pavarotti · Caballé · Ghiaurov · Krause · Pears · LPO · Mehta are probably definitive, and have better sound quality as well (though still fall short of current state of the art, for the obvious reason that recording technology has progressed since the early 1970's). However, they typically cost as much each as this entire set.
(If one wants all three of them, buying the boxed set that contains them will cost about the same as buying those three separately, and one will get two more operas, in which one can hear that Pavarotti was singing past his prime Puccini: The Definitive Collection, though it seems not to have bothered many of his fans. The operas that that set lacks that this Tebaldi set has are, in my opinion, less famous and well-known for good reason, but it obviously hurts nothing to have more, and others may disagree with my opinion on this matter. Interestingly, that set is the same label, Decca, as this Tebaldi set.)
So, should you buy this set? Well, they are great performances and the sound is very good. But they are not the very best performances of the operas that can be had (at least of the three mentioned above with Pavarotti in the early 1970's), and the sound quality isn't the best either, though as already stated repeatedly, they are great performances with good quality sound. The lack of libretti may also disappoint. But at this price, I think it can confidently be asserted, you will never do better. If the sets were the same price, I would recommend the other Decca set above, but it typically costs about three times as much and lacks four of the operas in this set. If you have the money and love Puccini (everyone should!), buy both sets. If you don't have the money for both sets, think carefully about what, exactly, matters most to you, and buy accordingly.
One more thing. If you order this set, like with all boxed sets, immediately when you receive it, check to make sure that all the CDs are there and seem to be in good condition. The first set I got from Amazon was missing a disc. But buying from Amazon is great, as they paid the return shipping for that set and sent me a replacement. 5 stars for Amazon.com!