Well, that's a "maybe". A drive of that era may well be using "LBA" as its communication method with the machine's controller. If so, you should have no trouble. BUT if it uses the older system of "C, H, S" settings, a modern enclosure's built-in controller probably cannot handle it.
Boot the old machine and go directly into BIOS Setup. Look at the first screen with HDD settings on it. For that drive, look at the parameters entered. If it has values entered under headings like Type (a 2-digit number less than 50), Cylinders, Heads, Sectors, and the last column has some odd mode setting, you could have a problem. But if the HDD type is "AUTO" and the last column says "LBA", or maybe "Large", you may be OK to move it to an enclosure.
If you want, report here exactly what that line or info says and we can advise.
If you are buying an enclosure, its internal interface MUST match the type of old HDD. I would assume that is IDE, and the standard 3½" wide HDD format. The external connection to your computer just needs to match the port(s) your computer has available. Almost all have USB2, some have either eSATA or IEEE 1394a (aka Firewire 400). Many enclosures come with two connection options, some with all three. You use only one at a time.