My equipment for reference:
Topping D10 and D30
Grace Design SDAC (Built in on the DROP Cavalli Tube Hybrid)
DROP Cavalli Tube Hybrid(CTH) with built in SDAC
Below are what I would recommend for someone new to the hobby:
I like D10 and D30 more than Grace SDAC, and I can't see how sound can improve further from D10 or D30, so I would definitely recommend them. only difference between D10 and D30 is input options.
(Budget) Monolith Spark, Any Schiit entry level solid state, JDS Atom. Buy these if you are on a budget of $100 to $200, or if you want to experience "upgrade"; it's like if your first car is a Mercedes Benz instead of a Civic, you wouldn't really know how nice the Mercedes Benz is.
(Preferred) SMSL SP200 THX, Drop 789 THX.
For how cheap these amps are now (~$259 and $299), I can't find any reason of getting other amps between $200 to $300. When I upgraded from budget SMSL SAPII, SMSL SP200 wasn't released, and DROP THX 789 was $399, and I found a CTH for $140 on eBay, that's why I went with it. If I am in the market again to upgrade from SAPII, i'd definitely go with THX amps listed above.
(Nostalgic) Darkvoice Tube Amp suppose to sound very nice with HD6XX, definitely one amp i'd like to get my hands on one day. But they run super hot, so may not be the most ideal daily use amp.
Sky is the limit with amps, but based on reviews I've read and watched, unless you have really well trained ears, you won't hear much difference past THX technology offered by SMSL or Drop.
I have not heard everything I have listed, but based on reviews of equipment I already have, and compare them to reviews of equipment I don't have by the same person, I can kinda tell what i would like and suggest others to buy.
Based on my own experience, i'd say Headphone accounts for 60% of the sound, 25% is amp, and 15% is DAC. So if you like the headphone to begin with, you are going to enjoy the music out of them as long as you have enough power to drive it.