You have a locked CPU on an H81 chipset - so won't be overclocking (so won't be increasing heat beyond 'stock') therefor, the stock cooler will suffice.
Are you certain you want to go liquid? The H55 is $60. Solid air coolers (for stock voltages) like the 212 EVO and Cryorig H7 are quality 'budget' air coolers in the $25-$35 range.