There isn't anything wrong with a box system that is made by a reputable manufacturer (Denon, HK, Yamaha, Onkyo, ect); however, if you get one like I did many moons ago, you might wonder why you don't feel "in" to the experience of being immersed in your movies or music.
That being said; when buying a new box system, you have a warranty, everything is included to hook up your system (save for cables on occasion and sources), and speakers are included that will work. Notice I said "work" in the effect that they will make noise and sound better than a set of integrated TV speakers.
A piece by piece is really the way to go, and after having experience with boxed systems and truely separate components, you have more control and tonal quality by piecing separates yourself. The easiest (or sometimes confusing) process is determining what you want your system to handle, source wise. Do you need it to be working alongside a display? Do you need some of the latest technological enhancements such as HDMI, scalers, or network capability? Do you want it for a garage or a home theater room? Is your room small or large and do you listen to audio at lower levels or do you like rocking the house to the foundation?
All these questions and probably many more that I didn't list become the basis for what you need to decide before looking at any equipment. It's like buying motorcycle when you need a vehicle capable of holding your five member household, and likewise buying a tank to remove a small tree in your back yard when you just need a chainsaw.
When all is said and done, though, my opinion is to get a receiver that is capable to handle what speakers you are looking at getting as well as being expandable for sources. I would personally get a receiver that has HDMI capability as well as pre-outs. Be aware that HDMI in receivers can vary as to handling decoding as well as upscaling; ask yourself what you need or if you are confused, ask us what HDMI type sources you are looking at getting (if any) and to what display you are going to use.
If HDMI isn't in you forseeable future or you don't want HDMI, at least get a reciever wth enough analog connectivity and pre-outs, as you can hook more things up later and still use the receiver as a pre-amp should you need or want to use it in conjunction with a power amplifier.
Speakers are the hardest part to choose from. There are so many of them out there, some good, some bad, and many overpriced for what quality they give you.
I would personally try to get a quality two channel system (with a subwoofer if your budget allows). Figure out if you want bookshelfs or floor standing speakers; I would go for higher quality bookshelfs as you can later use them as surround speakers.
Cables are simple. 16 AWG for speakers is fine. Some would argue 18 on the smaller side or 14-12 on the larger side. You can get this by a roll or in cut lengths at a hardware store. Interconnects are mainly overhyped. Get quality cables from Blue Jeans (a Audioholics sponsor and a reputable manufacturer) or Monoprice (better pricing, and still a great selection of quality cables).