The setup looks like a decent office build. There are a few things personally I would do differently, but I have set certain standards that I just don't ever come below when it comes to the custom computers our company builds.
On to your questions. First, the onboard graphics for the Intel HD is actually pretty nice if you're not doing demanding stuff. To ask if it's good enough we would have to know first what he is intending to do with it. In other words, is this basic web access, word processing, and bookkeeping? If so, then yes definitely. You can run two monitors off of the onboard graphics will no problem. However, if you are wanting to run three or more monitors on this computer, or are wanting to get into more demanding multimedia or graphics production work, or gaming, then you will need a dedicated graphics card. Again, which one to go with is going to depend upon the software you are intending to run.
Your second question is in regards to the best bang for the buck. This is gonna be a little harder to compare. Really, all the systems are pretty equal. The AM3+ six-core processor has the added benefit of additional processing cores, but there are not many basic business tasks which can utilize all those threads, so while it might offer better multi-threaded capabilities, I don't know if it would be the most efficient choice. Also, the graphics for that configuration is more limiting than the Intel or the FM2 platform selections. The AMD A10-5800K seems to be a very popular basic multimedia processor because it does have a quad-core chip with high clock speeds, and a powerful integrated graphics core. This gives you pretty great value. It has been a while since I have done anything on the AMD side for custom builds, personally, so I can't really give you much input on that. Our custom builds are based on the Intel platform like your first option.
Finally, longevity. This is a harder one to answer because two identical computers, running in identical environments and under identical situations should in theory last the exact same time, but this isn't the case. One may experience memory or hard drive failure, or even power supply or motherboard, after a year or two while the other computer may truck on for seven or more years. There are just too many unknowns. If you are referring to upgradability and the possibility of replacing parts into the future, then again it is going to be a toss up. Usually AMD tends to keep their platforms around longer, and be more cross-compatible, but Intel platforms have been going much the same way, and overall the general concept is clock-for-clock an Intel platform will be overall more efficient and powerful than a similar configured AMD platform. The difference is the AMD platform may cost a little less.
There are several small things to me that are red flags or concerns with the configurations you linked when it comes to business longevity. Again, a lot of this just comes from personal experience, testing, and preferences. But I think that any of the platform configurations you have quoted would be fine to use. My personal preference right now would say that the Intel would be your better option, though the AMD A10-5800K is definitely a possibility.