That thermal paste should be good enough. For a 3770k I would say a Hyper 212 EVO should be enough assuming you don't go crazy with the overclocks. The next step up I would consider the Xigmatek Dark Knight II Hawk Edition or the NZXT Havik 140. Last but not least the high end coolers, Noctua NH-D14, Thermalright Silver Arrow SB-E Extreme, and Phanteks PH-TC14PE.
These were ordered from lowest to highest price(s),