First headphones and amp combo?

Sennheiser headphones are great. I have had many pair over the decades. One comment is that the source and amplification are critical in having great sound. Typically I will have a ratio of 3x or more in electronics to headphone cost. You have to start somewhere. So what you propose may be a good start.  I started with headphones and a iPod during my most recent venture into headphones to get where I am now. (Click on my user ID to see my current setup).

This really needs to start with what sound characteristics you’re looking for.  The 6xx aren’t a good value if they don’t give you the right sound for your specific tastes. 

I have about a dozen sets of headphones including some "high end" ones including Audeze LCD-4, Sennheiser HD800, and Sony MDR-Z1R. 

The Sennheiser HD6XX get more use than any of my other headphones.  They are not the "best" sounding, but they are very easy to listen to and are super comfortable (I often wear them to bed).  I think they're hard to beat at their price point.  

I have no experience with the headphone amp you mentioned, but the amp does make a big difference.  The HD6XX will respond well if given good amplification.  I use the Sony TA-ZH1ES.

I hated headphones a decade ago and only gave it another go last year with the Meze Empyrean and Benchmark HPA4 amp. I loved this combo, It was super comfortable, fatigue free, and I would listen for hours late at night. Even falling asleep while listening in bed. Meze has a cheaper headphone for $299 that is supposed to be similar sonically to the Empy.

The Topping A90($599) was another amp I tried, and while it was not HPA4 caliber it was very close and much cheaper. I also had the Bryston BH-1 (sp?) headphone amp but found it a bit fatiguing.

Then this year I heard the RAAL SR1a headphones which are really nothing like headphones. More like 2 channel speakers on your ears, without room acoustics to deal with. I sold the Meze Empy and the HPA4 because I knew I would not be interested in any other headphones after the SR1a.

RAAL and Schitt are the only companies that sell a dedicated headphone amp for the SR1a. However, you can do what I do and use a 2 channel amp or integrated amp. So you can leverage your existing 2 channel amp for the RAAL. There is a amp interface box that makes this possibe. I use a dedicated 2 channel integrated amp (and sometimes amp) for my setup.

For regular headphones, I was debating between the HPA4 and the Headamp GS-X mini. Though I do not need either one now.

HeadAmp GS-X Mini Balanced Headphone Amplifier/Pre-Amp

I also bought for a friend the LSA headphones from UnderwoodHifi.com. That reminds me I need to help him set that up. He still has not heard the headphones 4 months later.