i7-3770
2x8GB DDR3 1333
Some light GPU, GT1030 maybe.
SATA SSD for the OS at least.
Limiting factor will be the OEM PSU if it is not ATX.
I don't think you will enjoy the dual core experience, thus the i7 suggestion. You may need to find a larger HP cooler, or adapt an aftermarket cooler to fit.
I have had good luck with adapting Deepcool Gammaxx 400 onto proprietary mounts. Just needed some m3 screws, nuts, and washers. (The key is to get several lengths of screws so that you can tighten them without bottoming out on the chassis side panel behind the motherboard tray)