Can you listen to a Grado at an audio shop? That was what I did in 2012, decided I liked the house sound and spent about $400 (a little more w/ a few accessories). A 400 budget for instance especially if you buy them used on the forums here could buy you a 225e (I have the earlier 225i and think it's good bang for buck) and a dac/amp combo. Lots of choices.
My suggestion would be a 225e ($200 new-but see if you can get it used) a Schiit modi DAC ($99 new which is killer value), and a Schiit Vali hybrid Tube amp ($119 new) or a Little Dot 1+ hybrid amp-just a little more than the Vali, or less if you buy it used. Both are tube hybrids and have really good synergy w/ Grados. I started with a Schiit Asgard-2 which is a nice little amp but I don't think has quite as good synergy.
Caveats: if you haven't heard Grados throw everything I just said out the window. All bets are off. You might not like their sound signature (some don't) or more commonly, you may find the headphones uncomfortable.
And, there are many, many more ways to mix and match HP/DAC/AMP. You could go for a DAC/AMP combo for instance.
If you get the 80i, you won't even need an amp and can save your money for something bigger down the road.