The 'full effect' comes down to :

- exactly which of those headphones you purchase

- your final budget : I think you will find that the amp you need is always a few hundred dollars more than the amp you can afford :)

When you start reading reviews of amps like the Eddie Current ZDT, and how well they light up the headphones you have listed, it may be difficult to realign your sights. At the other end of the fiscal scale, several people claim that their Fiio E9, a sub $200 amp, happily powers their K701s. Other budget possibilities may include the Corda Swing and the Purity Audio KICAS/Caliente, but so much of it depends on your personal musical preferences. An amp that some describe as 'detailed and insightful' might sound sterile to your ears - I have certainly fallen down that mineshaft with a previous amp purchase - so it pays to be clear on exactly what you want. 

The final piece of advice is to avoid taking advice from Grado owners. Shameless fanboys, the lot of em.