Typically, MOST carpets come in a 12 foot width. The architect that specified a 13 foot square foot room obviously wasn't thinking of carpet on the floors. Berbers will often come in a 15 foot width, so if you want a Berber, you can probably save on the cost of installation by opting for a 15 foot wide carpet. There was a time when 13 foot 6 inch wide carpets were not uncommon, but my understanding is that almost no one makes carpet in 13'6" width any more.
My personal experience with the big box stores is that they sell primarily Olefin carpets. Olefin is a fiber very similar to polypropylene. Olefin is the least expensive fiber used to make carpet, and so Olefin carpets are the least expensive to buy. One problem with Olefin carpets is that furniture will leave bad "dents" in the carpet where the furniture legs were, but those dents generally come out on their own within a few months. My experience with Olefin carpet in an apartment block is that they start showing traffic patterns in about 6 tp 7 years. They aren't long lived carpets.
If it were my house, I would install a nylon carpet. Nylon is the strongest fiber used to make carpet, and so nylon carpets are generally the longest wearing. Over 80% of the commercial carpet made and sold in the USA is made of nylon.
Now, DuPont has spent a king's ransom trying to make their Antron nylon more stain resistant. The result is DuPont's "StainMaster" nylon carpet, and it's expensive price tag is evidence of the amount of money DuPont has squandered on trying to make their 6,6 nylon stain resistant. Truth be told, DuPont has largely failed in their effort to make StainMaster carpets stain resistant. A far more effective way of making a nylon carpet stain resistant is to buy a carpet made of SOLUTION DYED nylon fiber.
Solution dyed nylon fiber is nylon to which extremely tiny coloured particles (called "pigments") have been added before the nylon is drawn into a fiber. The result is a strand of nylon plastic with tiny coloured particles suspended inside it very much like the raisins in raisin bread. The advantages of solution dyed nylon is that it gives you the strength and longitevity of a nylon carpet while also allowing you to use stain removal chemicals (like hydrogen peroxide) on the carpet to remove stains without removing the dye from the carpet fiber. Because the colour of the carpet is encased in nylon plastic, the stain removal chemicals never actually come into contact with the pigments that give the carpet it's colour, and so only the soil causing the stain is removed; not the colour of the carpet. (PS: the chemical used by carpet and upholstery cleaners to remove stains from upholstery and drapes is hydrogen peroxide, which you can buy at any drug store.)
So, if it was my house, I'd probably look for a 15 foot wide solution dyed nylon carpet, or go with a 12 foot wide carpet and buy extra to place a seam in that carpet to make it wider. Any place that sells carpet will know how to figure out how much more length you need to order the make that seam. With carpet, all of the tufts lean slightly in the direction the carpet came off the mill, so it's important that when putting a seam in a carpet, that the tufts in the pieces that get hot melt taped to the side of the carpet have their tufts going in the same direction as the main part of the carpet. If you don't ensure that, then each piece of carpet will have a slightly different apparent colour depending on which way the tufts on that piece of carpet are leaning.
Probably the longest wearing carpets are the level loop carpets. There's a natural resiliency to a loop that you don't have with cut pile carpets. A cut pile carpet is one where the tops of the tufts have been cut, allowing each fiber in each tuft to move independantly from all of the other fibers in the tuft. These kind of carpets are called "Plush" carpets. If you've ever vacuumed a carpet and noticed that the carpet colour changes depending on which direction the vaccuum cleaner was going when it passed over the carpet, then you've had first hand experience with a cut pile carpet. Level loop carpets won't do that.
A "Saxony" is just a cut pile carpet (like a Plush carpet) where the tufts are more tightly twisted and more closely packed together. Saxonly carpets cost more because you're getting more carpet fiber in every square yard of carpet.
In a bedroom, you'll normally be walking with bare or stocking feet, so a Plush or Saxony carpet fells softer and perhaps a bit warmer underfoot than a level loop carpet.
When it comes to underpad, you basically get the most bang for the buck with 7 or 8 pound per cubic foot underpads. When a flooring store offers "Free Underpad" with every carpet purchase, they're giving away 3 or 4 pound per cubic foot underpad. The denser the foam rubber of the underpad, the more energy the pad absorbs with every foot fall and the longer the carpet will last; up to a point... there are some premium underpads that cost just as much as cheap carpet, but they won't double or triple the lifespan of your carpet. You can get foam underpad where they use less blowing gas to make the foam, and the result is that the air bubbles in the foam don't intersect. The advantage of that is that the underpad is much more impermeable to liquid stains. These more impermeable pads are often called "Pet Pads" because they help prevent urine stains from pets from penetrating into the wood underlayment under the underpad; which can be an expensive proposition to replace. It's common to have houses where the owners had a dozen or more pet cats or dogs to have to replace the underlayment under the carpet to get rid of the urine smell in the house.
So, if it were my house, I'd go with a solution dyed nylon carpet. If I could find something I liked in a 15 foot width, I'd buy that and save the incremental cost of putting a seam in the carpet. If this is a bedroom, I wouldn't be hesitant to go for a Plush or Saxony carpet because bedrooms aren't high traffic areas and won't get as dirty as carpet in entrance ways. I'd go with a 7 or 8 pound per cubic foot underpad.
Finally, there's a popular misconception that shampooing a carpet gets it cleaner than vaccuuming. Truth is that a vaccuum cleaner and carpet shampoo'er are different tools meant to do different tasks. A vaccuum cleaner is meant to remove DRY soil from the carpet, like dirt tracked in on your shoes, dead skin cells, paper fibers, pollen and other dry dirt. A carpet shampoo'er is meant to remove wet or dried up liquid spills. If you don't believe me, next time you go to the beach, see if it's easier to remove sand from dry feet or wet feet. As soon as your carpet shampoo'er gets the carpet wet, it makes it difficult to remove solid soils like dead skin cells from the carpet because the surface tension of the water holds the dead skin cells to the carpet fibers like glue. This is the reason why every manufacturer of carpet shampooing equipment will recommend that you vaccuum the carpet with a good quality vaccuum cleaner BEFORE shampooing it. The best way of getting the longest lifespan out of your carpet is to vaccuum it regularily with a good quality vaccuum cleaner.
Hope this helps.