Okay, I'm back.
Carpet store vs. big box home improvement store -- well, since 99% of my experience has involved a big box, I'm slightly biased in that regard. The carpet store might have more of a selection but quality wise they're equal. Some carpet stores may also offer a lower grade pad with the option to upgrade to the grade of pad that the big box will offer as their initial option.
Definitely go with a 6 lb. pad for plush and a 7 lb. pad for berber. If you shop around, make sure to check on things like additional charge for removing the old carpet and pad, moving furniture, limits on what they will and will not move, etc.
In terms of softness, I like the soft nylons like Stainmaster's Tactesse. They have a great feel to them if that's what you're looking for. Many of the polyesters also have a soft feel and vibrant colors, especially the ones that are PET polyester. PETs are made from recycled plastic soda bottles.
Nylon is a strong fiber and keeps its like new appearance longer. It's also more expensive to produce, but worth the money. PET Polys are not quite as strong as the nylons but still very strong and are priced for someone on a budget. Olefin or polypropylene is naturally stain resistant and used a lot in berbers and commercial carpet, but can be a very rough fiber.
All of the big manufacturers -- Shaw, Mohawk, Beaulieu, Gulistan, and others -- make high-quality carpet. They all make carpet from branded and unbranded nylon. Branded would be like Stainmaster or Solutia WearDated nylon, unbranded is made by someone else or even by the manufacturer. Nylon is nylon and I really don't see much of a difference between branded and unbranded.
I don't know if that's answered all of your questions. It's hard to give an opinion or recommendation on specific carpet without seeing it in person. If you have any other questions, I'll be more than happy to help.
