You could do that for 200 dollars, but i myself do it through a laptop as already suggested.
the advantages of the laptop is that uses minimal power, quieter and maybe more easily hidden. you can also find good refurbished laptops for 200 dollars
googling inexpensive HTPC builds comes up with any info you need, i would use something like that as a starting point to thinking about where you want to go with it.
http://www.homemediatech.net/3-budget-htpc-builds-for-under-250-january-2015/1059
basically you don't need much, also with black friday and holiday shopping season coming you can usually find good deals. all you need is some cpu, ram, mobo (probably ITX the smallest form factor and then a cheap ITX case (match case size to mobo size adn match cpu socket to mobo socket and ram to mobo compatibility) usually have power supply included and some sort of storage)