Just about any non gaming machine will meet the spec you have given and click here is one example of what you can get on the High Street. If you are happy to buy from an internet supplier then there are plenty of similar machines around but you can't walk in and try them out.
In my opinion you should set your budget first and then buy the best machine you can afford rather than try and stretch to get "the latest and best" - you will always be behind the technology curve no matter how hard you try.
Packages will always be cheaper but you are stuck with the supplier's choice of monitor, keyboard and mouse which are not always the best choice - for example you might get a wired mouse and keyboard when wireless might suit you better or vice versa.
No you do not need Intel, AMD processors in budget applications are just as good and cheaper.
Good luck with the search.