I've never installed a "one piece" carpet, but I have seen them advertised. A place called Automotive Custom Carpet just a block from my house used to make these molded one piece carpets for just about any car made since the 60's. They do have a couple of advantages . . . they are one piece, and molded to fit the floor. They would probably be a breeze to install, and wouldn't have all of edges that might come loose in the stock style carpets. Even so, I'd prefer the stock multi-piece style. They are pretty easy to install, and if you ever need to do someting that requires working under the carpet (adjusting your shifter, replacing the shift rod bushing, replacing the brake line from the master cylinder to the back of the car, etc.) you don't have to remove the whole interior. With a one piece carpet, you would have to remove both seats, the panels under the rear seat, and the entire carpet to do any one of those jobs. With the stock style, you just peel back one or two pieces, do your work, and stick 'em back down with spray adhesive. Just be aware that there are lots of grades of the stock style carpets . . . You will be much happier with the finished look if you spend a little extra and get one with bound edges even if it's a cheap grade of carpet.
By the way, in addition to the glue, the originals had 3 or 4 upholstery tacks in the kick pannel pieces. If you just glue them in place, they will be falling off in a year or two.