ok, i think that you are asking for a lot for your budget. i also suspect you may be missing out on a key item.
- from what i know, an average (haswell) cpu like i3 costs about 7k - 10k. a good i5 costs about 11k thru 15k
- a good (1333 MHz) ram 4gb costs about 2k - 3k, although i recommend 8gb for you
- a basic (lga1150) b85 mobo costs about 5k - 7k, although i have not done enough research into h81 to know which one's better
- the most important thing for a good gaming experience is a graphics card, and i'm not sure if you already have it or have factored in out of your present budget, depending on your selection, it can cost as much as your cpu or more