You could try out the Schiit Audio line of products. Very highly regarded in the audiophile community.
Starting at 99 bux for more portable solid state dacs,dac/amps like the Fulla, the Modi, The Magni, ALL of which produce excellent quality sound, and then, as you graduate your desires, move up to the more mid- higher cost gear including some lovely sounding tube amps, like the Lyr, and the Valhalla, and the Mjolnir.
I am very very happy using a Magni/Modi on my somewhat confined computer desktop,(where I spend MUCH time working with images as an art photographer), when I want to lay back and listen in my leizure, I am using a Valhalla with a BiFrost DAC. The computer desktop gear plays my streaming stuff from my Mac, the bigger tube-amp gear runs either from the computer or the high res SACD player.
You also can't go wrong with WOO audio....but you start getting quite pricey,(worth it, as I can attest, owning many of Woo's very fine tube gear), and it starts to get very addictive/costly, what with tube rolling and cable upgrades and which amp for which headphones and things that hook you into years-long discussions over at HeadFi......LOL
As for headphones; I would say, upgrade according to your musical preferences.
Different KINDS of headphones do different things to the music, and not all lines of cans carry the same sound across their range. For instance; I too have Senns, I am into the 600's. I chose them over the "higher end" Senns, because I like how much more transparent they sound when playing classical music than do the 650's on up. The higher end Senns get more bass-y,(in a nice way, don't get me wrong), where the 600's are considered by many to be the more honest across the frequency range, with more power and a bit less veiled than the also quite nice 598's.
Grado cans have different sound sigs per set as well, and Grado aficionados will tell you that we have a different set of Grados for each type of music we listen to. I like my 325 metal backs for electronic music,(where sparkle and clarity shine), my RS1s for stringed instrument classical and acoustic....and I had another set of 325's modded with open wooden cups for a very lively, yet less "sparkling", somewhat more mellowed highs range.
And I RUN to my Beyerdynamic T1 teslas for anything where accuracy and speed and a very precise, nearly clinical presentation with a HUGE stage is desired. They may be my faves overall, simply because MY TASTE in how I hear music tends to appreciate a presentation that is clinical and accurate with MUCH clarity... and I replace the organic and warm that they may lack by using tube amps,(like Woo), to drive my T1's, when I am schmoozed back on my recliner, floating on a sound sea of dark polished wood cello a'la Truls Mørk...
I think starting with a line of products that offers a great range in choices, at high quality, and won't break you at the start is a good way to go, giving you a chance to explore just what you are looking for to produce a sound that YOU LIKE to hear. I think the reason I suggest sticking with a line of products from a single manufacturer, starting out, is that there DOES tend to be consistency in SS,(albeit some fundamental changes across the range, like the Senns dealie), and, when you are talking componants, like amps and dacs and stuff, they tend to play well together. so your whole rig will sing nicely, without too much tweaking and modding and tryingtofindtherightconnectorforthisohdamn!
Visit HeadFi. You can learn SO MUCH about EVERYTHING audio over there. We have threads and reviews for almost EVERY sound production device ever created, forums for DIY'ers, sections for REALLY EXPENSIVE gear, and a For Sale forum, where you may find upgrade gear that you want for less money than you worried about spending. Lots of folks over on HeadFi have already been upgrading for YEARS, and we often are happy to offer our previous, usually very nicely maintained, "lesser" gear at fair and decent prices there.
LONG reply, I know.
But I was once where you are. And I was glad other folks took the time to reply to me, help me out.
p.s. I personally don't like anything noise-cancelling, so Bose is typically out for me.
My speakers tend to be old Brits, like Celestions, or older build Polk Audio.